Effective interactions in lysozyme aqueous solutions: a small-angle neutron scattering and computer simulation study

We report protein-protein structure factors of aqueous lysozyme solutions at different pH and ionic strengths, as determined by small-angle neutron scattering experiments. The observed upturn of the structure factor at small wavevectors, as the pH increases, marks a crossover between two different regimes, one dominated by repulsive forces, and another one where attractive interactions become prominent, with the ensuing development of enhanced density fluctuations. In order to rationalize such experimental outcome from a microscopic viewpoint, we have carried out extensive simulations of different coarse-grained models. We have first studied a model in which macromolecules are described as soft spheres interacting through an attractive r(-6) potential, plus embedded pH-dependent discrete charges; we show that the uprise undergone by the structure factor is qualitatively predicted. We have then studied a Derjaguin-Landau-Verwey-Overbeek (DLVO) model, in which only central interactions are advocated; we demonstrate that this model leads to a protein-rich/protein-poor coexistence curve that agrees quite well with the experimental counterpart; experimental correlations are instead reproduced only at low pH and ionic strengths. We have finally investigated a third, "mixed" model in which the central attractive term of the DLVO potential is imported within the distributed-charge approach; it turns out that the different balance of interactions, with a much shorter-range attractive contribution, leads in this latter case to an improved agreement with the experimental crossover. We discuss the relationship between experimental correlations, phase coexistence, and features of effective interactions, as well as possible paths toward a quantitative prediction of structural properties of real lysozyme solutions.     

Equilibrium clusters in concentrated lysozyme protein solutions

We have studied the structure of salt-free lysozyme at 293 K and pH 7.8 using molecular simulations and experimental SAXS effective potentials between proteins at three volume fractions, ?=0.012, 0.033, and 0.12. We found that the structure of lysozyme near physiological conditions strongly depends on the volume fraction of proteins. The studied lysozyme solutions are dominated by monomers only for ?≤0.012; for the strong dilution 70% of proteins are in a form of monomers. For ?=0.033 only 20% of proteins do not belong to a cluster. The clusters are mainly elongated. For ?=0.12 almost no individual particles exits, and branched, irregular clusters of large extent appear. Our simulation study provides new insight into the formation of equilibrium clusters in charged protein solutions near physiological conditions.     

Preferential hydration of lysozyme in water/glycerol mixtures: a small-angle neutron scattering study

In solution small-angle neutron scattering has been used to study the solvation properties of lysozyme dissolved in water/glycerol mixtures. To detect the characteristics of the protein-solvent interface, 35 different experimental conditions (i.e., protein concentration, water/glycerol fraction in the solvent, content of deuterated compounds) have been considered and a suitable software has been developed to fit simultaneously the whole set of scattering data. The average composition of the solvent in the close vicinity of the protein surface at each experimental condition has been derived. In all the investigated conditions, glycerol resulted especially excluded from the protein surface, confirming that lysozyme is preferentially hydrated. By considering a thermodynamic hydration model based on an equilibrium exchange between water and glycerol from the solvation layer to the bulk, the preferential binding coefficient and the excess solvation number have been estimated. Results were compared with data previously derived for ribonuclease A in the same mixed solvent: even if the investigated solvent compositions were very different, the agreement between data is noticeable, suggesting that a unique mechanism presides over the preferential hydration process. Moreover, the curve describing the excess solvation number as a function of the solvent composition shows the occurrence of a region of maximal hydration, which probably accounts for the changes in protein stability detected in the presence of cosolvents.     

A small-angle X-ray scattering study of bromine-containing latex particles

A small-angle X-ray scattering (SAXS) study of two-stage latices (TSL), composed of polystyrene (PS) and polytribromostyrene (PTBrS), is presented. The analysis of the scattering curves leads to the conclusion that the TSL particles have a concentric core-shell structure. When a PTBrS latex was used as a seed, its particles were overcoated with a PS shell during the second-stage polymerization. However, only a small portion of the seed particles were overcoated with a PTBrS shell when using a PS seed. The size distributions of the TSL and the PTBrS latex particles were determined from the scattering curves, using the method of Indirect Fourier Transformation. The resulting average radii were in good agreement with the values obtained from TEM observations. © 1996 John Wiley & Sons, Inc.     

Cholesteric hydroxypropylcellulose solutions: Microscopy and small-angle light scattering

Polarized optical microscopy and small-angle light scattering (SALS) are used to investigate the cholesteric phase of aqueous hydroxypropylcellulose (HPC) solutions. The results suggest a polygonal focal conic rather than the recently proposed parabolic focal conic morphology. Measurements of the polygonal domain size show it to decrease with increasing HPC concentration. Depolarized SALS gives clover-leaf patterns, whose maximum of intensity at 45° is related to the domain size.     

A small-angle neutron scattering study of cholic acid-based organogel systems

Small-angle neutron scattering measurements were performed on some cholic acid-based gel systems in order to gain detailed information about the network structure. The presence of thin fibers with a radius of about 10-20 A was found for various gelators. Two types of interaction between different sorts of fibers were demonstrated, depending on the molecular structure of the gelator. The first type involves the presence of microcrystalline knots with a dimension of about 100-200 A between the fibers. Upon heating, this network gradually disintegrates. The second type involves loose entanglements between flattened fibers. The occurrence of these types of interaction is related to the length of the alkyl tail attached to cholic acid.     

A small-angle neutron scattering study on polydisperse silica spheres coated with polyisobutene

Neutron-scattering studies at small angles are performed on dilute dispersions of small, polydisperse silica spheres coated with polyisobutene in mixtures of h₁₂ and d₁₂-cyclohexane. The contrast variation method is applied to reveal the internal structure of the compound particles. For a detailed interpretation of the scattering curves, it is assumed that the particles consist of spherical silica cores with concentric PIB-layers into which solvent molecules can penetrate. Also the polydispersity of the particle cores is taken into account. Model calculations fit the experimental curves fairly well except for the curves near the matching point, and at higher wavevectors, where experimental errors are relatively large due to the smallness of the scattering of the particles compared to that of the background.     

Quasielastic small-angle neutron scattering from heavy water solutions of cyclodextrins

We present a model for quasielastic neutron scattering (QENS) by an aqueous solution of compact and inflexible molecules. This model accounts for time-dependent spatial pair correlations between the atoms of the same as well as of distinct molecules and includes all coherent and incoherent neutron scattering contributions. The extension of the static theory of the excluded volume effect [A. K. Soper, J. Phys.: Condens. Matter 9, 2399 (1997)] to the time-dependent (dynamic) case allows us to obtain simplified model expressions for QENS spectra in the low Q region in the uniform fluid approximation. The resulting expressions describe the quasielastic small-angle neutron scattering (QESANS) spectra of D(2)O solutions of native and methylated cyclodextrins well, yielding in particular translational and rotational diffusion coefficients of these compounds in aqueous solution. Finally, we discuss the full potential of the QESANS analysis (that is, beyond the uniform fluid approximation), in particular, the information on solute-solvent interactions (e.g., hydration shell properties) that such an analysis can provide, in principle.     

Reentrant phase behavior of nanoparticle solutions probed by small-angle scattering

The nanoparticles in solution represent a model system, where the well-established colloidal theories such as the Debye–Hückel theory and/or Derjaguin–Landau–Verwey–Overbeek theory can be implemented to predict the nanoparticle phase behavior. Recently, reentrant phase transitions in a wide range of colloids (e.g., inorganic and organic nanoparticles, polymers, and biomolecules) have been observed, which are not consistent with these theories. The colloids in the reentrant phase behavior undergo a phase change and return back to the original phase with respect to a specific physiochemical parameter (e.g., ionic strength, concentration of different additives, temperature, and so on). The nanoparticle–polymer/multivalent ion systems, demonstrating such phase transition and the corresponding phase behavior in terms of interparticle interactions, have been probed by small-angle scattering. It has been shown how the tuning in interparticle interactions using external parameters can lead to reentrant phase behavior and use the nanoparticle aggregation for building nanohybrids. The deviations of the present observations from those of the standard colloidal theories and the anticipated challenges are also discussed.     

Mesoscopic scale structures in self-organized surfactant solutions determined by small-angle neutron scattering

A novel procedure for SANS data analysis is described which enables one to use the fitted parameters to compute the average mean, Gaussian and square mean curvatures of the interface in systems which show a micro-phase-separated bicontinuous structure. This procedure also leads to a 3-D reconstruction of the connected internal interface which allows one to visualize the mesoscopic scale morphology of the material. The method has been successfully applied to various bicontinuous structures such as microemulsions made of surfactant, water and oil, porous silica glasses and phase-separated homopolymer blends. In this lecture, we show examples of analyses of SANS data taken from one-phase bicontinuous microemulsions at the hydrophile-lipophile-balance temperature and a light scattering intensity taken from a symmetric micro-phase-separated polymer blend at the late stage of spinodal decomposition.     

A small-angle neutron scattering study of poly(ethylene oxide) microstructure in aqueous poly(styrenesulfonate sodium) solutions

Dilute aqueous solutions of d-PEO and PSSNa mixtures were studied by (2)H NMR spectroscopy and small-angle neutron scattering (SANS). The interactions between d-PEO and PSSNa were found to be negligible both in the presence and absence of NaCl. At very dilute concentration (0.7 mg mL(-1)), d-PEO chains were still found to be slightly collapsed at ambient temperature in water. Upon the addition of PSSNa, aggregates of d-PEO were observed with d-PEO coils loosely associated with each other. The average centre to centre distance between d-PEO coils, which was calculated from the maxima in SANS spectra, was similar to the size of the individual coils. The effect of a simple salt, NaCl, on d-PEO-PSSNa interaction was investigated. Salt addition induced a breakdown of the dilute d-PEO aggregates.     

Interactions between block copolymers and single-walled carbon nanotubes in aqueous solutions: a small-angle neutron scattering study

The amphiphilic copolymers of the Pluronic family are known to be excellent dispersants for single-walled carbon nanotubes (SWCNT) in water, especially F108 and F127, which have rather long end-blocks of poly(ethylene oxide) (PEO). In this study, the structure of the CNT/polymer hybrid formed in water is evaluated by measurements of small-angle neutron scattering (SANS) with contrast variation, as supported by cryo-transmission electron microscopy (cryo-TEM) imaging. The homogeneous, stable, inklike dispersions exhibited very small isolated bundles of carbon nanotubes in cryo-TEM images. SANS experiments were conducted at different D(2)O/H(2)O content of the dispersing solvent. The data for both systems showed surprisingly minimal intensity values at 70% D(2)O solvent composition, which is much higher than the expected value of 17% D(2)O that is based on the scattering length density (SLD) of PEO. At this near match point, the data exhibited a q(-1) power law relation of intensity to the scattering vector (q), indicating rodlike entities. Two models are evaluated, as extensions to Pederson's block copolymer micelles models. One is loosely adsorbed polymer chains on a rodlike CNT bundle. In the other, the hydrophobic block is considered to form a continuous hydrated shell on the CNT surface, whereas the hydrophilic blocks emanate into the solvent. Both models were found to fit the experimental data reasonably well. The model fit required special considerations of the tight association of water molecules around PEO chains and slight isotopic selectivity.     

A small-angle neutron scattering study of adsorbed polymer structure in concentrated colloidal dispersions

Poly(ethylene oxide) (PEO) adsorption on colloidal silica particles was studied by small-angle neutron scattering under the core-contrast-matching condition. The volume fraction profile of the adsorbed layer was derived by modeling the average layer scattering term. It was found that, with increasing colloid concentration, the adsorbed PEO layers collapse due to the repulsions between adsorbed layers on neighboring particles. At the same time, the correlation length in the adsorbed layer obtained by fitting the layer fluctuation scattering term was found to decrease, indicating that denser polymer layers are formed. These two observations are self-consistent.     

A small-angle X-ray scattering study of the interactions in concentrated silica colloidal dispersions

The structure factors of colloidal silica dispersions at rather high volume fractions (from 0.055 to 0.22) were measured by small-angle X-ray scattering and fitted with both the equivalent hard-sphere potential model (EHS) and the Hayter-Penfold/Yukawa potential model (HPY). Both of these models described the interactions in these dispersions successfully, and the results were in reasonable agreement. The strength and range of the interaction potentials decreased with increasing particle volume fractions, which suggests shrinkage of the electrical double layer arising from an increase in the counterion concentration in the bulk solution. However, the interactions at the average interparticle separation increased as the volume fraction increased. The interaction ranges (delta) determined by the two models were very similar. Structure factors were also used to determine the size and volume fraction of the particles. The values of the size obtained from the structure factors were slightly larger than those obtained from the form factors; this difference is ascribed to the nonspherical shape and polydispersity of the colloidal particles. The volume fractions measured by these two methods were very similar and are both in good agreement with the independently measured results.     

A small-angle x-ray scattering study of starch gelatinization in excess and limiting water

The architecture of the starch granule, and its subsequent disruption due to the application of heat and water, known as gelatinization, is of wide interest. Small-angle x-ray scattering (SAXS) techniques have been used to study gelatinization in limiting and excess water. SAXS allows the absorption of water into the differing regions of the starch granule to be monitored. In excess water, a process of cooperative melting can be seen. In limiting water, the crystalline order melts at a higher temperature. These features have been studied, and observed features of the gelatinization related to those known from other techniques. © 1993 John Wiley & Sons, Inc.     

Direct methods in small-angle scattering

Direct methods of small-angle scattering data treatment and interpretation are reviewed. The possibilities of Tikhonov's regularization method for solving ill-posed experimental data processing problems (desmearing, size distribution functions evaluation) are shown; comparison with other data treatment methods is made. Methods for direct reconstruction of the structure of particles in isotropic monodisperse objects are presented. The cases of particles described by one- and two-dimensional density distributions and the possibilities of application of the multipole expansion theory are considered.     

Hydration and interactions in protein solutions containing concentrated electrolytes studied by small-angle scattering

During protein crystallization and purification, proteins are commonly found in concentrated salt solutions. The exact interplay of the hydration shell, the salt ions, and protein-protein interactions under these conditions is far from being understood on a fundamental level, despite the obvious practical relevance. We have studied a model globular protein (bovine serum albumin, BSA) in concentrated salt solutions by small-angle neutron scattering (SANS). The data are also compared to previous studies using SAXS. The SANS results for dilute protein solutions give an averaged volume of BSA of 91,700 ?(3), which is about 37% smaller than that determined by SAXS. The difference in volume corresponds to the contribution of a hydration shell with a hydration level of 0.30 g g(-1) protein. The forward intensity I(0) determined from Guinier analysis is used to determine the second virial coefficient, A(2), which describes the overall protein interactions in solution. It is found that A(2) follows the reverse order of the Hofmeister series, i.e. (NH(4))(2)SO(4) < Na(2)SO(4) < NaOAc < NaCl < NaNO(3) < NaSCN. The dimensionless second virial coefficient B(2), corrected for the particle volume and molecular weight, has been calculated using different approaches, and shows that B(2) with corrections for hydration and the non-spherical shape of the protein describes the interactions better than those determined from the bare protein. SANS data are further analyzed in the full q-range using liquid theoretical approaches, which gives results consistent with the A(2) analysis and the experimental structure factor.     

Micelle formation in sodium hexadecyl sulfate surfactant solutions studied by small-angle neutron scattering

Micelle formation in aqueous sodium hexadecyl sulfate solutions is studied by small-angle neutron scattering. Measurements are carried out at different concentrations (1.1, 2.2, 3.2, 5.4, 10.9 and 32.8 mM/dm³) and at different temperatures (40°, 50°, and 60°C). The monotonous evolution of interparticle correlation can be observed on the measured scattering patterns. At high concentrations (10.9 and 32.8 mM/dm³) scattering patterns are described by interacting ellipsoids, but at low concentrations by non-interacting ellipsoids. Computation of the distance distribution function proved the ellipsoidal shape at 10.9 and 32.8 mM/dm³, but showed an unexpectedly large particle dimension and elongation of the micelles at lower concentrations.     

A small-angle neutron scattering study of adsorbed poly(ethylene oxide) on Laponite

The adsorption of poly(ethylene oxide) (PEO) on synthetic anisotropic clay particles (Laponite) has been investigated as a function of the molecular weight. Contrast variation small-angle neutron scattering (SANS) measurements were used to characterize the distribution and adsorbed amount of polymer on the particles. These experiments show not only that polymer is present on the face of the clay particle but that it also extends or "wraps" over the edges. The edge layer was thicker than the face layer for all the molecular weights studied. The polymer layers are unusually thin, with a thickness and adsorbed amount that show little variation with molecular weight.     

A small-angle x-ray scattering study of blends of isotactic and atactic polystyrene

Small-angle x-ray scattering (SAXS) from blends of isotactic and atactic polystyrene has been studied. Results have been interpreted and compared using the Tsvankin, Vonk, and Hosemann techniques. The studies suggest that segregation of the atactic component occurs during crystallization within the growing spherulite of the isotactic component. However, since the interlamellar distance does not increase with atactic content, segregation is believed to occur with the formation of domains larger than interlamellar but smaller than spherulite size.