Static structure factor and collective diffusion of globular proteins in concentrated aqueous solution

The Salt-Induced Diffusiophoresis of Nonionic Micelles-Does the Salt-Induced Growth of Micelles Influence Diffusiophoresis?

Salt-induced diffusiophoresis is the migration of a colloidal particle in water due to a directional salt concentration gradient. An important example of colloidal particles is represented by micelles, generated by surfactant self-assembly in water. For non-ionic surfactants containing polyethylene glycol (PEG) groups, PEG preferential hydration at the micelle-water interface is expected to drive micelle diffusiophoresis from high to low salt concentration. However, micelles are reversible supramolecular assemblies, with salts being able to promote a significant change in micelle size. This phenomenon complicates the description of diffusiophoresis. Specifically, it is not clear to what extent the salt-induced growth of micelles affects micelle diffusiophoresis. In this paper, a multiple-equilibrium model is developed for assessing the contribution of the micelle growth and preferential hydration mechanisms to the diffusiophoresis of non-ionic micelles. The available experimental data characterizing the effect of NaCl on Triton X-100 aggregation number are combined with data on diffusiophoresis and the preferential hydration of PEG chains to show that the contribution of the micelle growth mechanism to overall diffusiophoresis is small compared to that of preferential hydration.

Design and Characterization of Model Systems that Promote and Disrupt Transparency of Vertebrate Crystallins In Vitro

Positioned within the eye, the lens supports vision by transmitting and focusing light onto the retina. As an adaptive glassy material, the lens is constituted primarily by densely-packed, polydisperse crystallin proteins that organize to resist aggregation and crystallization at high volume fractions, yet the details of how crystallins coordinate with one another to template and maintain this transparent microstructure remain unclear. The role of individual crystallin subtypes (α, β, and γ) and paired subtype compositions, including how they experience and resist crowding-induced turbidity in solution, is explored using combinations of spectrophotometry, hard-sphere simulations, and surface pressure measurements. After assaying crystallin combinations, β-crystallins emerged as a principal component in all mixtures that enabled dense fluid-like packing and short-range order necessary for transparency. These findings helped inform the design of lens-like hydrogel systems, which are used to monitor and manipulate the loss of transparency under different crowding conditions. When taken together, the findings illustrate the design and characterization of adaptive materials made from lens proteins that can be used to better understand mechanisms regulating transparency.

Protein solutions close to liquid-liquid phase separation exhibit a universal osmotic equation of state and dynamical behavior

Liquid-liquid phase separation (LLPS) of protein solutions is governed by highly complex protein-protein interactions. Nevertheless, it has been suggested that based on the extended law of corresponding states (ELCS), as proposed for colloids with short-range attractions, one can rationalize not only the thermodynamics, but also the structure and dynamics of such systems. This claim is systematically and comprehensively tested here by static and dynamic light scattering experiments. Spinodal lines, the isothermal osmotic compressibility κ_T and the relaxation rate of concentration fluctuations Γ are determined for protein solutions in the vicinity of LLPS. All these quantities are found to exhibit a corresponding-states behavior. This means that, for different solution conditions, these quantities are essentially the same if considered at similar reduced temperature or second virial coefficient. For moderately concentrated solutions, the volume fraction ϕ dependence of κ_T and Γ can be consistently described by Baxter's model of adhesive hard spheres. The off-critical, asymptotic T behavior of κ_T and Γ close to LLPS is consistent with the scaling laws predicted by mean-field theory. Thus, the present work aims at a comprehensive experimental test of the applicability of the ELCS to structural and dynamical properties of concentrated protein solutions.

Dense Phases of γ-Gliadins in Confined Geometries

The binary phase diagram of γ-gliadin, a wheat storage protein, in water was explored thanks to the microevaporator, an original PDMS microfluidic device. This protein, usually qualified as insoluble in aqueous environments, displayed a partial solubility in water. Two liquid phases, a very dilute and a dense phase, were identified after a few hours of accumulation time in the microevaporator. This liquid–liquid phase separation (LLPS) was further characterized through in situ micro-Raman spectroscopy of the dilute and dense protein phases. Micro-Raman spectroscopy showed a specific orientation of phenylalanine residues perpendicular to the PDMS surfaces only for the diluted phase. This orientation was ascribed to the protein adsorption at interfaces, which would act as nuclei for the growth of dense phase in bulk. This study, thanks to the use of both aqueous solvent and a microevaporator, would provide some evidence for a possible physicochemical origin of the gliadin assembly in the endoplasmic reticulum of albumen cells, leading to the formation of dense phases called protein bodies. The microfluidic tool could be used also in food science to probe protein–protein interactions in order to build up phase diagrams.

Effect of a Good buffer on the fate of metastable protein-rich droplets near physiological composition

Metastable protein-rich microdroplets are produced from liquid-liquid phase separation (LLPS) of protein aqueous solutions. These globules can be intermediates for the formation of other protein-rich phases. Lysozyme aqueous solutions undergo LLPS around 0 °C in the presence of NaCl near physiological conditions. Here, it is shown that insertion of small amounts of 4-(2-hydroxyethyl)-1-piperazineethanesulfonate (HEPES, 0.1 M) as a second additive to lysozyme-NaCl-water solutions near physiological ionic strength (0.2 M) is an essential step for triggering conversion of protein-rich droplets into another phase. Specifically, LLPS induced by cooling reproducibly leads to a rapid and high-yield formation of compact tetragonal crystalline microparticles only in the presence of HEPES. These microcrystals exhibit small size (1-3 μm), narrow size distribution and guest-binding properties. The temperature-concentration phase diagram shows a characteristic topology with LLPS boundary metastable with respect to tetragonal microcrystals, which in turn become less stable than rod-shaped orthorhombic crystals above 40 °C. Interestingly, dynamic light scattering, hydrogen-ion titrations and isothermal titration calorimetry reveal that lysozyme-HEPES interactions were found to be weakly attractive and exothermic. Our findings indicate that additives of salting-in type can represent an important factor controlling the fate of metastable protein-rich microdroplets relevant to drug formulations, femtosecond crystallography, and potential implications in protein-driven cytoplasmic compartmentalization.

Temperature Dependence of Protein Solution Viscosity and Protein-Protein Interactions: Insights into the Origins of High-Viscosity Protein Solutions

Protein solution viscosity (η) as a function of temperature was measured at a series of protein concentrations under a range of formulation conditions for two monoclonal antibodies (MAbs) and a globular protein (aCgn). Based on theoretical arguments, a strong temperature dependence for protein-protein interactions (PPI) indicates highly anisotropic, short-ranged attractions that could lead to higher solution viscosities. The semi-empirical Ross-Minton model was used to determine the apparent intrinsic viscosity, shape, and "crowding" factors for each protein as a function of temperature and formulation conditions. The apparent intrinsic viscosity was independent of temperature for aCgn, while a slight decrease with increasing temperature was observed for the MAbs. The temperature dependence of solution viscosity was analyzed using the Andrade-Eyring equation to determine the effective activation energy of viscous flow (E_a,η). While E_a,η values were different for each protein, they were independent of formulation conditions for a given protein. PPI were quantified via the osmotic second virial coefficient (B₂₂) and the protein diffusion interaction parameter (k_D) as a function of temperature under the same formulation conditions as the viscosity measurements. Net interactions ranged from strongly attractive to repulsive by changing formulation pH and ionic strength for each protein. Overall, larger activation energies for PPI corresponded to larger activation energies for η, and those were predictive of the highest η values at higher protein concentrations.

Potential and limits of a colloid approach to protein solutions

Looking at globular proteins with the eyes of a colloid scientist has a long tradition, in fact a significant part of the early colloid literature was focused on protein solutions. However, it has also been recognized that proteins are much more complex than the typical hard sphere-like synthetic model colloids. Proteins are not perfect spheres, their interaction potentials are in general not isotropic, and using theories developed for such particles are thus clearly inadequate in many cases. In this perspective article, we now take a closer look at the field. In particular, we reflect on the fact that modern colloid science has been undergoing a tremendous development, where a multitude of novel systems have been developed in the lab and in silico. During the last decade we have seen a rapidly increasing number of reports on the synthesis of anisotropic, patchy and/or responsive synthetic colloids, that start to resemble their complex biological counterparts. This experimental development is also reflected in a corresponding theoretical and simulation effort. The experimental and theoretical toolbox of colloid science has thus rapidly expanded, and there is obviously an enormous potential for an application of these new concepts to protein solutions, which has already been realized and harvested in recent years. In this perspective article we make an attempt to critically discuss the exploitation of colloid science concepts to better understand protein solutions. We not only consider classical applications such as the attempt to understand and predict solution stability and phase behaviour, but also discuss new challenges related to the dynamics, flow behaviour and liquid-solid transitions found in concentrated or crowded protein solutions. It not only aims to provide an overview on the progress in experimental and theoretical (bio)colloid science, but also discusses current shortcomings in our ability to correctly reproduce and predict the structural and dynamic properties of protein solutions based on such a colloid approach.

Anisotropic dynamics and kinetic arrest of dense colloidal ellipsoids in the presence of an external field studied by differential dynamic microscopy

Anisotropic dynamics on the colloidal length scale is ubiquitous in nature. Of particular interest is the dynamics of systems approaching a kinetically arrested state. The failure of classical techniques for investigating the dynamics of highly turbid suspensions has contributed toward the limited experimental information available up until now. Exploiting the recent developments in the technique of differential dynamic microscopy (DDM), we report the first experimental study of the anisotropic collective dynamics of colloidal ellipsoids with a magnetic hematite core over a wide concentration range approaching kinetic arrest. In addition, we have investigated the effect of an external magnetic field on the resulting anisotropic collective diffusion. We combine DDM with small-angle x-ray scattering and rheological measurements to locate the glass transition and to relate the collective short- and long-time diffusion coefficients to the structural correlations and the evolution of the zero shear viscosity as the system approaches an arrested state.

Understanding mAb aggregation during low pH viral inactivation and subsequent neutralization

Monoclonal antibodies (mAbs) and related recombinant proteins continue to gain importance in the treatment of a great variety of diseases. Despite significant advances, their manufacturing can still present challenges owing to their molecular complexity and stringent regulations with respect to product purity, stability, safety, and so forth. In this context, protein aggregates are of particular concern due to their immunogenic potential. During manufacturing, mAbs routinely undergo acidic treatment to inactivate viral contamination, which can lead to their aggregation and thereby to product loss. To better understand the underlying mechanism so as to propose strategies to mitigate the issue, we systematically investigated the denaturation and aggregation of two mAbs at low pH as well as after neutralization. We observed that at low pH and low ionic strength, mAb surface hydrophobicity increased whereas molecular size remained constant. After neutralization of acidic mAb solutions, the fraction of monomeric mAb started to decrease accompanied by an increase on average mAb size. This indicates that electrostatic repulsion prevents denatured mAb molecules from aggregation under acidic pH and low ionic strength, whereas neutralization reduces this repulsion and coagulation initiates. Limiting denaturation at low pH by d-sorbitol addition or temperature reduction effectively improved monomer recovery after neutralization. Our findings might be used to develop innovative viral inactivation procedures during mAb manufacturing that result in higher product yields.

Light Scattering to Quantify Protein-Protein Interactions at High Protein Concentrations

Static and dynamic (laser) light scattering (SLS and DLS, respectively) can be used to measure the so-called weak or colloidal protein-protein interactions in solution from low to high protein concentrations (c₂). This chapter describes a methodology to measure protein-protein self-interactions using SLS and DLS, with illustrative examples for monoclonal antibody solutions from low to high protein concentrations (c₂ ~ 1-10² g/L).

Protein-Protein Interactions of Highly Concentrated Monoclonal Antibody Solutions via Static Light Scattering and Influence on the Viscosity

The ability to design and formulate mAbs to minimize attractive interactions at high concentrations is important for protein processing, stability, and administration, particularly in subcutaneous delivery, where high viscosities are often challenging. The strength of protein-protein interactions (PPIs) of an IgG1 and IgG4 monoclonal antibody (mAb) from low to high concentration was determined by static light scattering (SLS) and used to understand viscosity data. The PPI were tuned using NaCl and five organic ionic co-solutes. The PPI strength was quantified by the normalized structure factor S(0)/ S(0)_HS and Kirkwood-Buff integral G₂₂/ G_22,HS (HS = hard sphere) determined from the SLS data and also by fits with (1) a spherical Yukawa potential and (2) an interacting hard sphere (IHS) model, which describes attraction in terms of hypothetical oligomers. The IHS model was better able to capture the scattering behavior of the more strongly interacting systems (mAb and/or co-solute) than the spherical Yukawa potential. For each descriptor of PPI, linear correlations were obtained between the viscosity at high concentration (200 mg/mL) and the interaction strengths evaluated both at low (20 mg/mL) and high concentrations (200 mg/mL) for a given mAb. However, the only parameter that provided a correlation across both mAbs was the oligomer mass ratio ( m_oligomer/ m_{monomer+dimer}) from the IHS model, indicating the importance of self-association (in addition to the direct influence of the attractive PPI) on the viscosity.

Statistical-thermodynamic model for light scattering from eye lens protein mixtures

We model light-scattering cross sections of concentrated aqueous mixtures of the bovine eye lens proteins γB- and α-crystallin by adapting a statistical-thermodynamic model of mixtures of spheres with short-range attractions. The model reproduces measured static light scattering cross sections, or Rayleigh ratios, of γB-α mixtures from dilute concentrations where light scattering intensity depends on molecular weights and virial coefficients, to realistically high concentration protein mixtures like those of the lens. The model relates γB-γB and γB-α attraction strengths and the γB-α size ratio to the free energy curvatures that set light scattering efficiency in tandem with protein refractive index increments. The model includes (i) hard-sphere α-α interactions, which create short-range order and transparency at high protein concentrations, (ii) short-range attractive plus hard-core γ-γ interactions, which produce intense light scattering and liquid-liquid phase separation in aqueous γ-crystallin solutions, and (iii) short-range attractive plus hard-core γ-α interactions, which strongly influence highly non-additive light scattering and phase separation in concentrated γ-α mixtures. The model reveals a new lens transparency mechanism, that prominent equilibrium composition fluctuations can be perpendicular to the refractive index gradient. The model reproduces the concave-up dependence of the Rayleigh ratio on α/γ composition at high concentrations, its concave-down nature at intermediate concentrations, non-monotonic dependence of light scattering on γ-α attraction strength, and more intricate, temperature-dependent features. We analytically compute the mixed virial series for light scattering efficiency through third order for the sticky-sphere mixture, and find that the full model represents the available light scattering data at concentrations several times those where the second and third mixed virial contributions fail. The model indicates that increased γ-γ attraction can raise γ-α mixture light scattering far more than it does for solutions of γ-crystallin alone, and can produce marked turbidity tens of degrees celsius above liquid-liquid separation.

Model for screened, charge-regulated electrostatics of an eye lens protein: Bovine gammaB-crystallin

We model screened, site-specific charge regulation of the eye lens protein bovine gammaB-crystallin (γB) and study the probability distributions of its proton occupancy patterns. Using a simplified dielectric model, we solve the linearized Poisson-Boltzmann equation to calculate a 54×54 work-of-charging matrix, each entry being the modeled voltage at a given titratable site, due to an elementary charge at another site. The matrix quantifies interactions within patches of sites, including γB charge pairs. We model intrinsic pK values that would occur hypothetically in the absence of other charges, with use of experimental data on the dependence of pK values on aqueous solution conditions, the dielectric model, and literature values. We use Monte Carlo simulations to calculate a model grand-canonical partition function that incorporates both the work-of-charging and the intrinsic pK values for isolated γB molecules and we calculate the probabilities of leading proton occupancy configurations, for 4<pH<8 and Debye screening lengths from 6 to 20 Å. We select the interior dielectric value to model γB titration data. At pH 7.1 and Debye length 6.0 Å, on a given γB molecule the predicted top occupancy pattern is present nearly 20% of the time, and 90% of the time one or another of the first 100 patterns will be present. Many of these occupancy patterns differ in net charge sign as well as in surface voltage profile. We illustrate how charge pattern probabilities deviate from the multinomial distribution that would result from use of effective pK values alone and estimate the extents to which γB charge pattern distributions broaden at lower pH and narrow as ionic strength is lowered. These results suggest that for accurate modeling of orientation-dependent γB-γB interactions, consideration of numerous pairs of proton occupancy patterns will be needed.

Concentration-Induced Association in a Protein System Caused by a Highly Directional Patch Attraction

Self-association of the protein lactoferrin is studied in solution using small-angle X-ray scattering techniques. Effective static structure factors have been shown to exhibit either a monotonic or a nonmonotonic dependence on protein concentration in the small wavevector limit, depending on salt concentration. The behavior correlates with a nonmonotonic dependence of the second virial coefficient on salt concentration, such that a maximum appears in the structure factor at a low protein concentration when the second virial coefficient is negative and close to a minimum. The results are interpreted in terms of an integral equation theory with explicit dimers, formulated by Wertheim, which provides a consistent framework able to explain the behavior in terms of a monomer-dimer equilibrium that appears because of a highly directional patch attraction. Short attraction ranges preclude trimer formation, which explains why the protein system behaves as if it were subject to a concentration-dependent isotropic protein-protein attraction. Superimposing an isotropic interaction, comprising screened Coulomb repulsion and van der Waals attraction, on the patch attraction allows for a semiquantitative modeling of the complete transition pathway from monomers in the dilute limit to monomer-dimer systems at somewhat higher protein concentrations.

Unusual liquid-liquid phase transition in aqueous mixtures of a well-known dendrimer

Liquid-liquid phase separation (LLPS) has been extensively investigated for polymer and protein solutions due to its importance in mixture thermodynamics, separation science and self-assembly processes. However, to date, no experimental studies have been reported on LLPS of dendrimer solutions. Here, it is shown that LLPS of aqueous solutions containing a hydroxyl-functionalized poly(amido amine) dendrimer of fourth generation is induced in the presence of sodium sulfate. Both the LLPS temperature and salt-dendrimer partitioning between the two coexisting phases at constant temperature were measured. Interestingly, our experiments show that LLPS switches from being induced by cooling to being induced by heating as the salt concentration increases. The two coexisting phases also show opposite temperature response. Thus, this phase transition exhibits a simultaneous lower and upper critical solution temperature-type behavior. Dynamic light-scattering and dye-binding experiments indicate that no appreciable conformational change occurs as the salt concentration increases. To explain the observed phase behavior, a thermodynamic model based on two parameters was developed. The first parameter, which describes dendrimer-dendrimer interaction energy, was determined by isothermal titration calorimetry. The second parameter describes the salt salting-out strength. By varying the salting-out parameter, it is shown that the model achieves agreement not only with the location of the experimental binodal at 25 °C but also with the slope of this curve around the critical point. The proposed model also predicts that the unusual temperature behavior of this phase transition can be described as the net result of two thermodynamic factors with opposite temperature responses: salt thermodynamic non-ideality and salting-out strength.

Protein-protein interactions in dilute to concentrated solutions: α-chymotrypsinogen in acidic conditions

Protein-protein interactions were investigated for α-chymotrypsinogen by static and dynamic light scattering (SLS and DLS, respectively), as well as small-angle neutron scattering (SANS), as a function of protein and salt concentration at acidic conditions. Net protein-protein interactions were probed via the Kirkwood-Buff integral G22 and the static structure factor S(q) from SLS and SANS data. G22 was obtained by regressing the Rayleigh ratio versus protein concentration with a local Taylor series approach, which does not require one to assume the underlying form or nature of intermolecular interactions. In addition, G22 and S(q) were further analyzed by traditional methods involving fits to effective interaction potentials. Although the fitted model parameters were not always physically realistic, the numerical values for G22 and S(q → 0) were in good agreement from SLS and SANS as a function of protein concentration. In the dilute regime, fitted G22 values agreed with those obtained via the osmotic second virial coefficient B22 and showed that electrostatic interactions are the dominant contribution for colloidal interactions in α-chymotrypsinogen solutions. However, as protein concentration increases, the strength of protein-protein interactions decreases, with a more pronounced decrease at low salt concentrations. The results are consistent with an effective "crowding" or excluded volume contribution to G22 due to the long-ranged electrostatic repulsions that are prominent even at the moderate range of protein concentrations used here (<40 g/L). These apparent crowding effects were confirmed and quantified by assessing the hydrodynamic factor H(q → 0), which is obtained by combining measurements of the collective diffusion coefficient from DLS data with measurements of S(q → 0). H(q → 0) was significantly less than that for a corresponding hard-sphere system and showed that hydrodynamic nonidealities can lead to qualitatively incorrect conclusions regarding B22, G22, and static protein-protein interactions if one uses only DLS to assess protein interactions.

Intermolecular interactions of IgG1 monoclonal antibodies at high concentrations characterized by light scattering

Light scattering intensity measurements of solutions of two purified monoclonal antibodies were performed over a wide range of concentrations (0.5-275 mg/mL) and ionic strengths (0.02 to 0.6 M). Despite extensive sequence homology between these mAbs, alteration of ∼20 amino acids in the complementarity determining regions resulted in different net intermolecular interactions and responses to solution ionic strength. The concentration dependence of scattering was analyzed by comparison with the predictions of three models, allowing for intermolecular interaction of various types. In order of increasing complexity, the three models account for: (1) steric repulsions (simple hard-sphere model), (2) steric repulsion with short-ranged attractive interactions of varying magnitude (adhesive hard-sphere model), and (3) steric and nonsteric repulsive interactions between several species whose relative concentrations may change as a function of total protein concentration as dictated by equilibrium self-association (effective hard-sphere mixture model). Simple scattering models of noninteracting and adhesive hard-sphere species permitted qualitative interpretation of contributions from excluded volume, electrostatic, and van der Waals interactions on net mAb interactions at high concentration as a function of ionic strength. mAb2 electrostatic interactions were repulsive, whereas mAb1 interactions were net attractive at low ionic strengths, attributed to an anisotropic distribution of molecular charge. The effective hard-sphere mixture model can account quantitatively for the dependence of scattering for both antibodies over the entire concentration range and at salt concentrations exceeding 40 mM. This analysis showed that at high ionic strength both mAbs self-associate weakly to form dimer with an affinity that varies little with salt concentration at concentrations exceeding 75 mM. In addition, mAb1 appears to self-associate further to form oligomers with stoichiometry of 4-6 and an affinity that declines substantially with increasing ionic strength. All three models lead to the conclusion that at high concentrations repulsive interactions are predominantly due to excluded volume, whereas additional features are salt-dependent and reflect a substantial electrostatic contribution to intermolecular interactions of both mAbs.

Small-angle X-ray scattering studies of the intact eye lens: effect of crystallin composition and concentration on microstructure

BACKGROUND

The cortex and nucleus of eye lenses are differentiated by both crystallin protein concentration and relative distribution of three major crystallins (alpha, beta, and gamma). Here, we explore the effects of composition and concentration of crystallins on the microstructure of the intact bovine lens (37 degrees C) along with several lenses from Antarctic fish (-2 degrees C) and subtropical bigeye tuna (18 degrees C).

METHODS

Our studies are based on small-angle X-ray scattering (SAXS) investigations of the intact lens slices where we study the effect of crystallin composition and concentration on microstructure.

RESULTS

We are able to distinguish the nuclear and cortical regions by the development of a characteristic peak in the intensity of scattered X-rays. For both the bovine and fish lenses, the peak corresponds to that expected for dense suspensions of alpha-crystallins.

CONCLUSIONS

The absence of the scattering peak in the nucleus indicates that there is no characteristic wavelength for density fluctuations in the nucleus although there is liquid-like order in the packing of the different crystallins. The loss in peak is due to increased polydispersity in the sizes of the crystallins and due to the packing of the smaller gamma-crystallins in the void space of alpha-crystallins.

GENERAL SIGNIFICANCE

Our results provide an understanding for the low turbidity of the eye lens that is a mixture of different proteins. This will inform design of optically transparent suspensions that can be used in a number of applications (e.g., artificial liquid lenses) or to better understand human diseases pathologies such as cataract.

Beneficial effect of solubility enhancers on protein crystal nucleation and growth

Crystallizing solutions of proteins often contain various nonelectrolyte additives that arise from the purification process of proteins or from the reagents employed in the screening kits. Currently, limited knowledge exists about the influence of these additives on the mechanisms underlying the crystallization process, in particular on the nucleation stage of crystals. To address this need, we studied crystallization of two proteins, D-xylose isomerase and chicken egg-white lysozyme, in small batches and in the presence of two solubility-enhancing additives, acetonitrile and glycerol. We have also measured the nucleation rates of crystals of these proteins in the presence and in the absence of acetonitrile using the method of initial rates. With the addition of the solubility enhancers, both proteins exhibited an increase in crystal nucleation at any given supersaturation. Solubility enhancing additives appear to lower the energy barrier to nucleation by influencing the strength of attraction between the protein molecules. We have characterized the quality of D-xylose isomerase crystals by determining the crystal mosaicity, which showed considerable improvement for crystals grown in the presence of additives. When compared to the crystals of chicken egg-white lysozyme, D-xylose isomerase crystals required higher supersaturations to nucleate. We attribute this result to the large size of the D-xylose isomerase molecule, which influences the energy barrier to nucleation by increasing the surface area of the critical nucleus. Contrary to the common expectation that reagents that solubilize the protein may hinder the crystallization process, our results suggest that solubility enhancers, in fact, can have a beneficial effect on the nucleation and growth of crystals. These findings are of importance in formulating successful strategies toward crystallizing new proteins.

Altered phase diagram due to a single point mutation in human gammaD-crystallin

The P23T mutant of human gammaD-crystallin (HGD) is associated with cataract. We have previously investigated the solution properties of this mutant, as well as those of the closely related P23V and P23S mutants, and shown that although mutations at site 23 of HGD do not produce a significant structural change in the protein, they nevertheless profoundly alter the solubility of the protein. Remarkably, the solubility of the mutants decreases with increasing temperature, in sharp contrast to the behavior of the native protein. This inverted solubility corresponds to a strong increase in the binding energy with temperature. Here we have investigated the liquid-liquid coexistence curve and the diffusivity of the P23V mutant and find that these solution properties are unaffected by the mutation. This means that the chemical potentials in the solution phase are essentially unaltered. The apparent discrepancy between the interaction energies in the solution phase, as compared with the solid phase, is explicable in terms of highly anisotropic interprotein interactions, which are averaged out in the solution phase but are fully engaged in the solid phase.

Liquid-liquid phase separation and static light scattering of concentrated ternary mixtures of bovine alpha and gammaB crystallins

We have used light scattering, turbidimetry, and thermodynamic analysis to study the phase diagram of concentrated aqueous mixtures of the bovine lens proteins, gammaB crystallin, and alpha crystallin. We find that dilute alpha crystallin raises the phase separation temperature of concentrated gammaB crystallin, while more concentrated alpha crystallin suppresses phase separation. Very concentrated alpha/gammaB mixtures can reversibly cloud above 37 degrees C, even though gammaB alone phase separates only below temperatures near 0 degrees C, and alpha does not phase separate. At the scattering vector magnitude used, high-concentration alpha/gammaB mixtures scatter less light than the weighted average of their component alpha and gammaB solutions, while low-concentration alpha/gammaB mixtures scatter more than such a weighted average. We use a mean-field thermodynamic analysis of such ternary mixtures to show that the observed light scattering and phase boundaries of alpha and gammaB crystallin mixtures give evidence for prominent local fluctuations of relative protein composition. In the single phase, these fluctuations scatter comparatively little light, but are associated with enhanced thermodynamic instability. By applying this analysis to the experimental tie lines we estimate the magnitude of the saddlelike component of the free energy near the aqueous-gammaB critical point.

Microscopic diffusion and hydrodynamic interactions of hemoglobin in red blood cells

The cytoplasm of red blood cells is congested with the oxygen storage protein hemoglobin occupying a quarter of the cell volume. The high protein concentration leads to a reduced mobility; the self-diffusion coefficient of hemoglobin in blood cells is six times lower than in dilute solution. This effect is generally assigned to excluded volume effects in crowded media. However, the collective or gradient diffusion coefficient of hemoglobin is only weakly dependent on concentration, suggesting the compensation of osmotic and friction forces. This would exclude hydrodynamic interactions, which are of dynamic origin and do not contribute to the osmotic pressure. Hydrodynamic coupling between protein molecules is dominant at short time- and length scales before direct interactions are fully established. Employing neutron spin-echo-spectroscopy, we study hemoglobin diffusion on a nanosecond timescale and protein displacements on the scale of a few nanometers. A time- and wave-vector dependent diffusion coefficient is found, suggesting the crossover of self- and collective diffusion. Moreover, a wave-vector dependent friction function is derived, which is a characteristic feature of hydrodynamic interactions. The wave-vector and concentration dependence of the long-time self-diffusion coefficient of hemoglobin agree qualitatively with theoretical results on hydrodynamics in hard spheres suspensions. Quantitative agreement requires us to adjust the volume fraction by including part of the hydration shell: Proteins exhibit a larger surface/volume ratio compared to standard colloids of much larger size. It is concluded that hydrodynamic and not direct interactions dominate long-range molecular transport at high concentration.

Protein diffusion coefficients determined by macroscopic-gradient Rayleigh interferometry and dynamic light scattering

Dynamic light scattering (DLS) is extensively used for measuring macromolecule diffusion coefficients. Contrary to classical techniques based on macroscopic concentration gradients, DLS probes microscopic fluctuations in concentration. DLS accuracy and its concordance with macroscopic-gradient techniques remains an outstanding important issue. We measured lysozyme diffusion coefficients in aqueous salt using both DLS and Rayleigh interferometry, a highly accurate macroscopic-gradient technique. The precision of our results is unprecedented. We find that our DLS values were systematically 2% higher than interferometry values. We believe that our interferometric measurements have produced the most accurate diffusion data ever reported for a protein, providing a new standard for quality control of DLS measurements. Furthermore, by interferometry, we have determined the whole diffusion coefficient matrix required for rigorously describing lysozyme-salt coupled diffusion. For the first time, we experimentally demonstrate that DLS does not provide the protein diffusion coefficient but one eigenvalue of the diffusion coefficient matrix.

Existence of hydration forces in the interaction between apoferritin molecules adsorbed on silica surfaces

The atomic force microscope, together with the colloid probe technique, has become a very useful instrument to measure interaction forces between two surfaces. Its potential has been exploited in this work to study the interaction between protein (apoferritin) layers adsorbed on silica surfaces and to analyze the effect of the medium conditions (pH, salt concentration, salt type) on such interactions. It has been observed that the interaction at low salt concentrations is dominated by electrical double layer (at large distances) and steric forces (at short distances), the latter being due to compression of the protein layers. The DLVO theory fits these experimental data quite well. However, a non-DLVO repulsive interaction, prior to contact of the protein layers, is observed at high salt concentration above the isoelectric point of the protein. This behavior could be explained if the presence of hydration forces in the system is assumed. The inclusion of a hydration term in the DLVO theory (extended DLVO theory) gives rise to a better agreement between the theoretical fits and the experimental results. These results seem to suggest that the hydration forces play a very important role in the stability of the proteins in the physiological media.

Protein crystal nucleation: is the pair interaction potential the primary determinant of kinetics?

Fundamental understanding of protein crystal nucleation facilitates crystallization of biological macromolecules for structure determination and control of crystal size distribution. In the studies presented here, nucleation kinetics of hen egg-white lysozyme crystals were measured at solution conditions that exhibited equal solubility by adjusting pH, temperature, or sodium chloride concentration. It was observed that solution conditions that lead to equal solubility resulted in equal nucleation rates and hence kinetic parameters. Since the solubility of globular proteins correlates with the osmotic second virial coefficient, B(22), an integral measure of the protein pair interaction potential, this observation indicates that the protein pair interaction plays a key role in determining nucleation kinetic parameters.

Prediction of collective diffusion coefficient of bovine serum albumin in aqueous electrolyte solution with hard-core two-Yukawa potential

A new method to predict concentration dependence of collective diffusion coefficient of bovine serum albumin (BSA) in aqueous electrolyte solution is developed based on the generalized Stokes-Einstein equation which relates the diffusion coefficient to the osmotic pressure. The concentration dependence of osmotic pressure is evaluated using the solution of the mean spherical approximation for the two-Yukawa model fluid. The two empirical correlations of sedimentation coefficient are tested in this work. One is for a disordered suspension of hard spheres, and another is for an ordered suspension of hard spheres. The concentration dependence of the collective diffusion coefficient of BSA under different solution conditions, such as pH and ionic strength is predicted. From the comparison between the predicted and experimental values we found that the sedimentation coefficient for the disordered suspension of hard spheres is more suitable for the prediction of the collective diffusion coefficients of charged BSA in aqueous electrolyte solution. The theoretical predictions from the hard-core two-Yukawa model coupled with the sedimentation coefficient for a suspension of hard spheres are in good agreement with available experimental data, while the hard sphere model is unable to describe the behavior of diffusion due to its neglect of the double-layer repulsive charge-charge interaction between BSA molecules.

Optimized Baxter model of protein solutions: Electrostatics versus adhesion

A theory is set up of spherical proteins interacting by screened electrostatics and constant adhesion, in which the effective adhesion parameter is optimized by a variational principle for the free energy. An analytical approach to the second virial coefficient is first outlined by balancing the repulsive electrostatics against part of the bare adhesion. A theory similar in spirit is developed at nonzero concentrations by assuming an appropriate Baxter model as the reference state. The first-order term in a functional expansion of the free energy is set equal to zero which determines the effective adhesion as a function of salt and protein concentrations. The resulting theory is shown to have fairly good predictive power for the ionic-strength dependence of both the second virial coefficient and the osmotic pressure or compressibility of lysozyme up to about 0.2 volume fraction.

Structure of peptide solutions: a light scattering and numerical study

We investigated the interactions between protein molecules in solution, in particular for low salt concentrations and thus strong electrostatic interactions where a treatment based on the second virial coefficient is not sufficient. Static and dynamic light scattering experiments on solutions containing the peptide human calcitonin (hCT) were combined with calculations based on the Ornstein-Zernike equation with the hypernetted chain (HNC) closure and computer simulations within the primitive electrolyte model. The simulation illustrates the distribution of proteins in solution and the formation of (transient) protein aggregates. It furthermore allows us to predict the physical stability of hCT solutions in dependence of ionic strength, pH and hCT concentration.

Thermodynamic instability in supersaturated lysozyme solutions: effect of salt and role of concentration fluctuations

Experimental and theoretical work has suggested that protein crystal nucleation can be affected by the separation of two metastable liquid phases with different local concentrations, or more specifically by critical density fluctuations. We measure the amplitude and correlation length of local concentration fluctuations by light scattering for supersaturated solutions of hen egg-white lysozyme (at pH 4.5 and at different NaCl concentrations, up to 7% w/v). By extrapolating the critical divergent behavior of concentration fluctuation amplitude versus temperature, we determine the spinodal line, that is the limit of stability. Cloud-point measurements are used to determine liquid-liquid coexistence, consistent with previous work. In the present work, which is an extensive study of off-critical fluctuations in supersaturated protein solution, we observe a nonclassical scaling divergent behavior of the correlation length of concentration fluctuations, thus suggesting that off-critical fluctuations may have a role in crystallization kinetics. To appropriately fit the spinodal data, an entropic term must be added to the van der Waals or to the adhesive hard-sphere model. We interpret this contribution as due to the salt-induced modulation of protein hydration.

Effective charges of colloidal particles obtained from collective diffusion experiments

In this work, the collective diffusion coefficient of highly charged colloidal particles in dilute dispersions has been measured by means of dynamic light scattering. The possibility of obtaining valuable information about the particle charge from these data is looked into with the help of electrophoresis experiments. Our results suggest that this is possible in the case of slight or moderately interacting particles as long as experimental data are properly treated. For highly interacting colloids, however, such information could not be so reliable, presumably due to certain shortcomings of the experimental technique at low angle. The role of charge renormalization is also discussed in this work.

Cold cataracts: a naturally occurring aqueous two-phase system

The cytoplasm of the eye lenses shows a liquid-liquid phase transition similar to the one observed in aqueous two-phase systems. This phenomenon is known as cold cataracts. We have studied the solution behavior of the main protein fractions that constitute the lenses' cytoplasm using small-angle neutron scattering and dynamic light scattering. Our results provide evidence that an intricate balance of forces underlines the physical phenomena responsible for the optical properties of the lenses and for the phase transition that is observed as the temperature is lowered below some critical value. These forces include solvent-mediated forces besides the more conventional Coulombic and dispersion forces. This study suggests that solvent mediated forces must be included to successfully model liquid-liquid phase transitions like the ones observed in cold cataracts or in aqueous two-phase systems.

Effect of glycerol on the interactions and solubility of bovine pancreatic trypsin inhibitor

The effects of additives used to stabilize protein structure during crystallization on protein solution phase behavior are poorly understood. Here we investigate the effect of glycerol and ionic strength on the solubility and strength of interactions of the bovine pancreatic trypsin inhibitor. These two variables are found to have opposite effects on the intermolecular forces; attractions increase with [NaCl], whereas repulsions increase with glycerol concentration. These changes are mirrored in bovine pancreatic trypsin inhibitor solubility where the typical salting out behavior for NaCl is observed with higher solubility found in buffers containing glycerol. The increased repulsions induced by glycerol can be explained by a number of possible mechanisms, all of which require small changes in the protein or the solvent in its immediate vicinity. Bovine pancreatic trypsin inhibitor follows the same general phase behavior as other globular macromolecules where a robust correlation between protein solution second virial coefficient and solubility has been developed. This study extends previous reports of this correlation to solution conditions involving nonelectrolyte additives.

A small-angle neutron scattering study of gamma-crystallins near their isoelectric point

In this paper, a small-angle neutron scattering study of gammaII-crystallins near their isoelectric point is presented. The experiments were carried out using protein concentrations of 5.7-85.7 mg/ml at temperatures in the range 11 -60 degrees C. The experimental data were analyzed using an ellipsoidal model for intraparticle correlations and the mean spherical approximation for interparticle correlations. Our studies revealed that gammaII-crystallins have a thick hydration layer, which is possibly due to the special arrangement of polar and ionic groups on their surface. The temperature scan shows that, as a result of relatively strong attractive forces, clusters of two, three, or higher oligomers are present below 20 degrees C. Our results suggest that protein clusters, with a distinctive hydration layer, form a protein-rich phase that separates from a protein-lean phase as the temperature is decreased below some threshold value.