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.     

A small-angle scattering study on equilibrium clusters in lysozyme solutions

We use small-angle scattering experiments to investigate the structural properties of aqueous lysozyme solutions under conditions where the existence of equilibrium clusters has recently been demonstrated (Nature 2004, 432, 492). We also discuss the possible emergence of a low angle scattering contribution, which recently attracted interest due to its appearance in solutions of various proteins. We demonstrate that in lysozyme solutions under our experimental conditions such rising low q intensities can only be observed under special circumstances and can thus not be attributed to the existence of a universal long-range attraction. We then focus on the structural properties of the equilibrium clusters as a function of protein concentration, temperature, and ionic strength. We show that the experimental structure factors obtained from the scattering measurements exhibit the typical cluster-cluster peak q(c) reflecting the mean distance between charged clusters as well as a monomer-monomer peak q(m), which represents the nearest neighbor shell of monomers within a single cluster. The underlying principle for the formation of these structures is the coexistence of two opposing forces, a short-range attraction and a long-range repulsion due to residual charges. We can quantitatively analyze our scattering data by applying a simple equilibrium cluster model and calculate an average cluster aggregation number, N(c). The thus obtained cluster aggregation number increases linearly with volume fraction. We also observe an increasing N(c) as temperature decreases and as the screening of residual charges increases. We point out the importance of the existence of equilibrium clusters and the universality of this phenomenon for self-assembling processes observed in nature. Finally, we discuss the limitations of our simple globular cluster model in view of recent findings from computer simulations.     

Microcalorimetric study of thermal unfolding of lysozyme in water/glycerol mixtures: an analysis by solvent exchange model

Folded protein stabilization or destabilization induced by cosolvent in mixed aqueous solutions has been studied by differential scanning microcalorimetry and related to difference in preferential solvation of native and denatured states. In particular, the thermal denaturation of a model system formed by lysozyme dissolved in water in the presence of the stabilizing cosolvent glycerol has been considered. Transition temperatures and enthalpies, heat capacity, and standard free energy changes have been determined when applying a two-state denaturation model to microcalorimetric data. Thermodynamic parameters show an unexpected, not linear, trend as a function of solvent composition; in particular, the lysozyme thermodynamic stability shows a maximum centered at water molar fraction of about 0.6. Using a thermodynamic hydration model based on the exchange equilibrium between glycerol and water molecules from the protein solvation layer to the bulk, the contribution of protein-solvent interactions to the unfolding free energy and the changes of this contribution with solvent composition have been derived. The preferential solvation data indicate that lysozyme unfolding involves an increase in the solvation surface, with a small reduction of the protein-preferential hydration. Moreover, the derived changes in the excess solvation numbers at denaturation show that only few solvent molecules are responsible for the variation of lysozyme stability in relation to the solvent composition.     

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.     

Structural behaviour of mixed cationic surfactant micelles: a small-angle neutron scattering study

Self-assembly in mixtures of two single-chain cationic surfactants, with different tail lengths (CTAB and DTAB) as well as of a single-chain (DTAB) and a double-chain (DDAB) cationic surfactant, with identical tail lengths, have been investigated with small-angle neutron scattering (SANS) and rationalised in terms of bending elasticity properties. The growth behaviour of micelles with respect to surfactant composition appears completely different in the two surfactant mixtures. DTAB form small oblate spheroidal micelles in presence of [NaBr] = 0.1 M that transform into prolate spheroidal mixed CTAB/DTAB micelles upon adding moderate amounts of CTAB, so as to give a mole fraction y = 0.20 in solution. Most unexpectedly, upon further addition of CTAB the mixed CTAB/DTAB micelles grow with an almost equal rate in both length and width directions to form tablets. In contrast to this behaviour, mixed DDAB/DTAB micelles grow virtually exclusively in the length direction, in presence of [NaBr] = 0.1 M, to form elongated ellipsoidal (tablet-shaped) and subsequently long wormlike micelles as the fraction of DDAB in the micelles increases. Mixed DDAB/DTAB micelles grow to become as long as 2000 Å before an abrupt transition to large bilayer structures occurs. This means that the micelles are much longer at the micelle-to-bilayer transition as compared to the same mixture in absence of added salt. It is found that the point of transition from micelles to bilayers is significantly shifted towards higher fractions of aggregated DTAB as an appreciable amount of salt is added to DDAB/DTAB mixtures, indicating a considerable reduction of the spontaneous curvature with an increasing [NaBr]. By means of deducing the various bending elasticity constants from our experimental results, according to a novel approach by ours, we are able to conclude that the different growth behaviours appear as a consequence of a considerably lower bending rigidity, as well as higher saddle-splay constant, for DDAB/DTAB surfactant mixtures in presence of [NaBr] = 0.1 M, as compared to mixtures of CTAB/DTAB in [NaBr] = 0.1 M and DDAB/DTAB in absence of added salt.     

A small-angle neutron scattering study of the ethyl (n-octyl) phosphate micelles in water

Summary Mixed-double chain anionic surfactants, barium- and lithium-salts of ethyl(n-octyl) phosphate (EOP), which are asymmetric in the molecular shape, and a series of identical chain di-n-alkyl phosphate lithium salts have been synthezized. The limiting partial molar volume of a PO ₄ ^– group (23.43±0.41 cm³ mol^–1) for use in small-angle neutron scattering analysis was determined by density measurements of a series of identical chain di-n-alkyl phosphate lithium salts. For lithium EOP-D₂O system, a critical micellar concentration (2.3 wt%) was determined by³¹P NMR spectra. The micellar shape and size in the EOP-water binary system has been investigated by using small-angle neutron scattering (SANS) spectra. It has been found that the micelles of barium EOP in water have the shape of a prolate spheroid and aggregation numbers (n) equal to 48 at 23°C and 52 at 50°C. For the lithium EOP-micellar system, it has been found that the minimum micelle with an aggregation numbern=21 is spherical and micellar growth and variation from the spherical to the prolate shape might occur with an increase in concen tration above the CMC.     

Mixed spherical and wormlike micelles: a contrast-matching study by small-angle neutron scattering

Small-angle neutron scattering studies were used to investigate the effect of adding an alcohol ethoxylate nonionic surfactant (d-C12E20) to aqueous solutions of a cationic surfactant, erucyl bis(hydroxyethyl) methylammonium chloride (EHAC), with and without salt (KCl). The systematic use of contrast-matching, by alternately highlighting or hiding one of the surfactants, confirms that mixed micelles are formed. In salt-free solutions, mixed spherical micelles are formed and a core-shell model combined with a Hayter-Penfold potential was used to describe the data. The core radius is dominated by the EHAC tails and the outer radius determined by the ethoxylate headgroups of the nonionic surfactant. Addition of KCl promotes micellar growth; however, results of varying the solvent contrast revealed that when the nonionic surfactant is incorporated into the wormlike structure micellar breaking is promoted. Thus, mixed wormlike micelles with shorter contour lengths compared to the pure EHAC worms are formed.     

Amphiphilic networks based on cross-linked star polymers: a small-angle neutron scattering study

Four different polymer model networks of identical molecular architecture based on cross-linked stars (CLSs) were investigated by small-angle neutron scattering (SANS). One of the model networks was a hydrophilic homopolymer CLS of 2-(dimethylamino)ethyl methacrylate (DMAEMA), and the other three were amphiphilic copolymer CLS co-networks of DMAEMA and hydrophobic methyl methacrylate (MMA): one based on a star with random copolymer arms and the other two based on heteroarm star copolymers. For the homopolymer and random copolymer star networks, the scattering curves show shoulders at low values of the scattering vector, indicating very small compacted domains with radii of 1.0-1.3 nm, with the random copolymer star co-network having somewhat larger domains. For the heteroarm star co-networks, pronounced peak maxima are observed because of a much higher degree of microphase structuring than for the other two co-networks. The scattering patterns are described by the presence of well-defined hydrophobic domains with radii of 7.1 and 10.3 nm in the two heteroarm star co-networks, respectively, thereby proving pronounced microphase separation in these systems.     

Sphere-to-rod transition of non-surface-active amphiphilic diblock copolymer micelles: a small-angle neutron scattering study

Micellization behavior of amphiphilic diblock copolymers with strong acid groups, poly(hydrogenated isoprene)-block-poly(styrenesulfonate), was investigated by small-angle neutron scattering (SANS). We have reported previously (Kaewsaiha, P.; Matsumoto, K.; Matsuoka, H. Langmuir 2005, 21, 9938) that this strongly ionic amphiphilic diblock copolymer shows almost no surface activity but forms micelles in water. In this study, the size, shape, and internal structures of the micelles formed by these unique copolymers in aqueous solution were duly investigated. The SANS data were well described by the theoretical form factor of a core-shell model and the Pedersen core-corona model. The micellar shape strongly depends on the hydrophobic chain length of the block copolymer. The polymer with the shortest hydrophobic chain was suggested to form spherical micelles, whereas the scattering curves of the longer hydrophobic chain polymers showed a q-1 dependence, reflecting the formation of rodlike micelles. Furthermore, the addition of salt at high concentration also induced the sphere-to-rod transition in micellar shape as a result of the shielding effect of electrostatic repulsion. The corona thickness was almost constant up to the critical salt concentration (around 0.2 M) and then decreased with further increases in salt concentration, which is in qualitatively agreement with existing theories. The spherical/rodlike micelle ratio was also constant up to the critical salt concentration and then decreased. The micelle size and shape of this unique polymer could be described by the common concept of the packing parameter, but the anomalously stable nature of the micelle (up to 1 M NaCl) is a special characteristic.     

Time-resolved small-angle neutron scattering study of polyethylene crystallization from solution

With time-resolved small-angle neutron scattering (TR-SANS), the crystallization kinetics of polyethylene from deuterated o-xylene solutions upon a temperature jump have been investigated. On the basis of a morphological model of coexisting lamellar stacks and coil chains in solution, experimental data have been quantitatively analyzed to provide structural information, such as the lamellar long period, the lamellar crystal thickness, the thickness of the amorphous layers between lamellae, the degree of crystallinity, and the crystal growth rate at various degrees of undercooling. The viability of TR-SANS for studying polymer crystallization is demonstrated through the consistency of these measurements and well-established knowledge of polyethylene crystallization from xylene solutions. One unique feature of this experimentation is that both the growth of lamellar crystals and the condensation of coil chains from solution are monitored simultaneously. The ratio of the crystal growth to the chain consumption rate decreases rapidly with a decreasing degree of undercooling. The Avrami analysis suggests that the growth mechanism approaches two-dimensional behavior at higher temperatures, and this is consistent with the observation of an increasing ratio of the sharp-surface area to the bulk crystal growth rate with temperature. The limitations, possible remedies, and potentials of TR-SANS for studying polymer crystallization are discussed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3133–3147, 2004     

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 and static light scattering study of micelles formed in aqueous mixtures of a nonionic alkylglucoside and an anionic surfactant

The size and shape of micelles formed in aqueous mixtures of the anionic surfactant sodium dodecyl sulfate (SDS) and the nonionic sugar-based surfactant n-decyl beta-D-glucopyranoside (C(10)G) at different concentrations of added salt have been investigated with small-angle neutron and static light scattering. Rather small prolate ellipsoidal micelles form in the absence of added salt and at [NaCl] = 10 mM in D(2)O. The micelles grow considerably in length to large rods as the electrolyte concentration is raised to [NaCl] = 0.1 M. In excess of nonionic surfactant ([SDS]/[C(10)G] = 1:3) at [NaCl] = 0.1 M in D(2)O, several thousands of Angstroms long wormlike micelles are observed. Most interestingly, a conspicuously large isotope solvent effect was observed from static light scattering data according to which micelles formed at [SDS]/[C(10)G] = 1:3 and [NaCl] = 0.1 M in H(2)O are at least five times smaller than micelles formed in the corresponding samples in D(2)O.     

Applications of small-angle X-ray scattering/small-angle neutron scattering and cryogenic transmission electron microscopy to understand self-assembly of surfactants

The self-assembling structures and dynamics of surfactants determine most of their macroscopic physicochemical properties and performances. Herein, we review recent work on the self-assembly of surfactants by small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) in conjunction with cryogenic transmission electron microscopy (Cryo-TEM) from the perspective of researchers having only limited theoretical knowledge of these techniques but expert in surfactants. Emphasis is placed on the structural analysis of typical surfactant aggregates over a wide range of size scales from nanometers up to microns, including spherical and rod-like micelles, wormlike micelles, vesicles, liquid crystals and coacervates, by combining different numerical approaches to the treatment of small-angle scattering data with the direct Cryo-TEM imaging method. Furthermore, the complementarity between SAXS and SANS, and between the scattering techniques and Cryo-TEM, that is, specific contributions of these techniques, is also covered.     

Microstructure of beta-lactoglobulin/pectin coacervates studied by small-angle neutron scattering

Small-angle neutron scattering (SANS) has been used to investigate the microstructure of beta-lactoglobulin/pectin coacervates prepared by different initial protein/polysaccharide weight ratio (r), sodium chloride concentration (C(NaCl)), and pectin charge density. The higher r and higher pectin charge density lead to higher scattering intensity at small q range (0.007 Angstrom(-1) < q < 0.02 Angstrom(-1)), suggesting that the charges of pectin chains are screened significantly by the binding of oppositely charged protein molecules, leading to a tighter aggregation of pectin chains. On the other hand, the appearance of a shoulder peak at intermediate q range (0.04 Angstrom(-1) < q < 0.2 Angstrom(-1)) is used to interpret the formation of protein domains in beta-lactoglobulin/pectin coacervates. At C(NaCl) = 0.1 M, the coacervate of beta-lactoglobulin and pectin A does not show a shoulder peak at intermediate q range at r = 10:1, suggesting that protein molecules are separately bound on pectin chains. However, a shoulder peak appears at intermediate q range at r = 20:1 and 30:1, and the average protein domain size estimated from the shoulder peak position is 7.2 and 8.5 nm, respectively, for these two coacervates. When C(NaCl) increases from 0.05 to 0.2 M, the shoulder peak shifts toward smaller q and becomes broader, indicating that the addition of a higher amount of salt leads to a more heterogeneous coacervate structure. Pectin B with a lower linear charge density favors the formation of larger protein domains. The formation of protein domains in beta-lactoglobulin/pectin coacervates is partially ascribed to the self-aggregation of beta-lactoglobulin molecules. Two kinds of microstructures of beta-lactoglobulin/pectin coacervates with and without observable protein domains have been proposed.     

Partitioning of macrocyclic compounds in a cationic and an anionic micellar solution: a small-angle neutron scattering study

Following a previous investigation on partitioning of some macrocycle compounds in sodium dodecyl sulfate (SDS) and dodecyltrimethylammonium bromide (DTAB) aqueous solutions and their effect on the micellar structure, a small-angle neutron scattering (SANS) study has been performed at fixed surfactant content (0.20 mol/L) and varying macrocycle concentrations from 0.20 up to 1.0 mol/L. Conductivity measurements have been also performed in order to evaluate the effect of the presence of macrocycles on the critical micellar concentration (cmc) of the two surfactants. SANS experimental data were fitted successfully by means of a core-plus-shell monodisperse prolate ellipsoid model. It has been found that 1,4,7,10,13,16-esaoxacyclooctadecane (18C6) and 4,7,13,16-tetraoxa-1,10-diazacyclooctadecane (22) do not interact with DTAB micelles whereas their sodium complexes interact with SDS aggregates and partially localize, as a consequence of electrostatic interaction, on the micellar surface or in the Stern layer. 2,5,8,11,14,17-Hexaoxabicyclo[16.4.0] dicosane (B18C6), as a consequence of the increased hydrophobic character with respect to 18C6, interacts with DTAB hydrocarbon chains and partially localizes in the inner part of micelles. This finding has been successfully used to justify the higher amount of B18C6 compared to the 18C6 one found in the SDS micellar phase. The substituted crown ether has been found localized both on the micelle surface via complex formation and in the inner part of micelles as a consequence of the increased hydrophobic character. For all systems, the aggregate size primarily decreases with the amount of macrocycle in the micellar phase. The interpretation of cmc trends as a function ofmacrocycle concentration gives information on its distribution between micellar and aqueous phases that is in line with SANS results.     

Characterization of polystyrene networks by small-angle neutron scattering

Polystyrene networks prepared by anionic polymerization have been characterized by small-angle neutron scattering. Two kinds of systems have been examined: (A) networks with labelled branch points allowing characterization of the spatial distribution of crosslinking points; (B) networks containing a low proportion of chains labelled with perdeuterated polystyrene in order to characterize the conformation of individual elastic chains of the polymeric network. The dependence of the results on swelling and uniaxial extension is discussed.     

Structure and dynamics of halogenoethanol-water mixtures studied by large-angle X-ray scattering, small-angle neutron scattering, and NMR relaxation

To clarify the structure of solvent clusters formed in halogenoethanol-water mixtures at the molecular level, large-angle X-ray scattering (LAXS) measurements have been made at 298 K on 2,2,2-trifluoroethanol (TFE), 2,2,2-trichloroethanol (TCE), and their aqueous mixtures in the TFE and TCE mole fraction ranges of 0.002 < or = x(TFE) < or = 0.9 and 0.5 < or = x(TCE) < or = 0.9, respectively. The radial distribution functions (RDFs) for TFE-water mixtures have shown that the structural transition from inherent TFE structure to the tetrahedral-like structure of water takes place at x(TFE) approximately 0.2. In the TCE-water mixtures inherent TCE structure remains in the range of 0.5 < or = x(TCE) < or = 1. Small-angle neutron scattering (SANS) experiments have been performed on CF(3)CH(2)OD- (TFE-d(1)-) D(2)O and CF(3)CD(2)OH- (TFE-d(2)-) H(2)O mixtures in the TFE mole fraction range of 0.05 < or = x(TFE) < or = 0.8. The SANS results in terms of the Ornstein-Zernike correlation length have revealed that TFE and water molecules are most heterogeneously mixed with each other in the TFE-water mixture at x(TFE) approximately 0.15, i.e., both TFE clusters and water clusters are most enhanced in the mixture. To evaluate the dynamics of TFE and ethanol (EtOH) molecules in TFE-water and ethanol-water mixtures, respectively, (1)H NMR relaxation rates for the methylene group within alcohol molecules have been measured by using an inversion-recovery method. The alcohol concentration dependence of the relaxation rates for the TFE-water and ethanol-water mixtures has shown a break point at x(TFE) approximately 0.15 and x(EtOH) approximately 0.2, respectively, where the structural transition from alcohol clusters to the tetrahedral-like structure of water takes place. On the basis of the present results, the most likely structure models of solvent clusters predominantly formed in TFE-water and TCE-water mixtures are proposed. In addition, effects of halogenation of the hydrophobic groups on clustering of alcohol molecules are discussed from the present results, together with the previous ones for ethanol-water and 1,1,1,3,3,3-hexafluoro-2-propanol- (HFIP-) water mixtures.     

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.