“Ordered” structure in solutions and gels of a globular protein as studied by small angle neutron scattering

Bayesian analysis of static light scattering data for globular proteins

Static light scattering is a popular physical chemistry technique that enables calculation of physical attributes such as the radius of gyration and the second virial coefficient for a macromolecule (e.g., a polymer or a protein) in solution. The second virial coefficient is a physical quantity that characterizes the magnitude and sign of pairwise interactions between particles, and hence is related to aggregation propensity, a property of considerable scientific and practical interest. Estimating the second virial coefficient from experimental data is challenging due both to the degree of precision required and the complexity of the error structure involved. In contrast to conventional approaches based on heuristic ordinary least squares estimates, Bayesian inference for the second virial coefficient allows explicit modeling of error processes, incorporation of prior information, and the ability to directly test competing physical models. Here, we introduce a fully Bayesian model for static light scattering experiments on small-particle systems, with joint inference for concentration, index of refraction, oligomer size, and the second virial coefficient. We apply our proposed model to study the aggregation behavior of hen egg-white lysozyme and human γS-crystallin using in-house experimental data. Based on these observations, we also perform a simulation study on the primary drivers of uncertainty in this family of experiments, showing in particular the potential for improved monitoring and control of concentration to aid inference.

Molecular Characterization of Polymer Networks

Polymer networks are complex systems consisting of molecular components. Whereas the properties of the individual components are typically well understood by most chemists, translating that chemical insight into polymer networks themselves is limited by the statistical and poorly defined nature of network structures. As a result, it is challenging, if not currently impossible, to extrapolate from the molecular behavior of components to the full range of performance and properties of the entire polymer network. Polymer networks therefore present an unrealized, important, and interdisciplinary opportunity to exert molecular-level, chemical control on material macroscopic properties. A barrier to sophisticated molecular approaches to polymer networks is that the techniques for characterizing the molecular structure of networks are often unfamiliar to many scientists. Here, we present a critical overview of the current characterization techniques available to understand the relation between the molecular properties and the resulting performance and behavior of polymer networks, in the absence of added fillers. We highlight the methods available to characterize the chemistry and molecular-level properties of individual polymer strands and junctions, the gelation process by which strands form networks, the structure of the resulting network, and the dynamics and mechanics of the final material. The purpose is not to serve as a detailed manual for conducting these measurements but rather to unify the underlying principles, point out remaining challenges, and provide a concise overview by which chemists can plan characterization strategies that suit their research objectives. Because polymer networks cannot often be sufficiently characterized with a single method, strategic combinations of multiple techniques are typically required for their molecular characterization.

Controlled Loading and Release of Beta-Lactoglobulin in Calcium-Polygalacturonate Hydrogels

We show here how the structure of polygalacturonate (polyGalA) hydrogels cross-linked by Ca²⁺ cations via external gelation controls the loading and release rate of beta-lactoglobulin (BLG), a globular protein. Hydrogels prepared from a polyGalA/BLG solution are found to be similar to those obtained from a polyGalA solution in our previous study (Maire du Poset et al. Biomacromolecules 2019, 20 (7), 2864-2872): they exhibit similar transparencies and gradients of mechanical properties and polyGalA concentrations. The nominal BLG/polyGalA ratio of the mixtures is almost recovered within the whole mixed hydrogel despite such strong concentration gradients, except in the part of the hydrogels with the largest mesh size, where more BLG proteins are present. This gradient enables one to tune the amount of protein loaded within the hydrogel. At a local scale, the proteins are distributed evenly within the hydrogel network, as shown by small-angle neutron scattering (SANS). The release of proteins from hydrogels is driven by Fickian diffusion, and the release rate increases with the mesh size of the network, with a characteristic time of a few hours. The specific structure of these polysaccharide-based hydrogels allows for control of both the dosage and the release rate of the loaded protein and makes them good candidates for use as oral controlled-delivery systems.

Alkali cold gelation of whey proteins. Part II: Protein concentration

The effect of the whey protein isolate (WPI) concentration on the sol-gel-sol transition in alkali cold gelation was investigated at pH 11.6-13 using oscillatory rheometry. The elastic modulus increases quickly with time to reach a local maximum (G'max), followed by a degelation step where the modulus decreases to a minimum value (G'min). Depending on the pH, a second gelation step will occur. At the end of the first gelation step around G'max, the system fulfilled the Winter-Chambon criterion of gelation. The analysis of the maximum moduli with the protein concentration shows that (i) there is a percolation concentration above which an elastic response is observed (approximately 6.8 wt %); (ii) there are two concentration regimes for G''max and G''max above this concentration, where we have considered power-law and percolation equations; (iii) there is a crossover concentration between the two regimes (at approximately 8 wt %) for both G'max and G''max when both moduli are equal, and this value is constant under all conditions tested (G'max=G''max approximately 4 Pa). Therefore, alkali cold gelation is better represented using two concentrations regimes than one, as observed for other biopolymers.

The influence of electrostatic interaction on the structure and the shear modulus of heat-set globular protein gels

Gels formed by the globular protein β-lactoglobulin after heat denaturation were studied using light scattering, turbidity and shear oscillation measurements. The structure of the gels was characterized in terms of the amplitude and the correlation length of concentration fluctuations. The strength of electrostatic interactions was varied by changing the pH in the absence of added salt or by changing the NaCl concentration at pH 7. A very strong increase of the heterogeneity of the gels was observed when decreasing the pH towards the isoelectric point or when increasing the salt concentration. The structural change was interpreted in terms of a decrease of the net repulsion between the growing aggregates leading to increased concentration fluctuations and finally microscopic phase separation. The elastic shear modulus increased with decreasing pH and showed a maximum as a function of the NaCl concentration. No direct correlation between the change in the structure and the elastic modulus was found.

Light-scattering study of the structure of aggregates and gels formed by heat-denatured whey protein isolate and beta-lactoglobulin at neutral pH

The structure of aggregates and gels formed by heat-denatured whey protein isolate (WPI) has been studied at pH 7 and different ionic strengths using light scattering and turbidimetry. The results were compared with those obtained for pure beta-lactoglobulin (beta-Lg). WPI aggregates were found to have the same self-similar structure as pure beta-Lg aggregates. WPI formed gels above a critical concentration that varied from close to 100 g/L in the absence of added salt to about 10 g/L at 0.2 M NaCl. At low ionic strength (<0.05 M NaCl) homogeneous transparent gels were formed, while at higher ionic strength the gels became turbid but had the same self-similar structure as reported earlier for pure beta-Lg. The length scale characterizing the heterogeneity of the gels increased exponentially with increasing NaCl concentration for both WPI and pure beta-Lg, but the increase was steeper for the former.

Ground-state clusters for short-range attractive and long-range repulsive potentials

We report calculations of the ground-state energies and geometries for clusters of different sizes (up to 80 particles), where individual particles interact simultaneously via a short-ranged attractive potential, modeled with a generalization of the Lennard-Jones potential, and a long-ranged repulsive Yukawa potential. We show that for specific choices of the parameters of the repulsive potential, the ground-state energy per particle has a minimum at a finite cluster size. For these values of the parameters in the thermodynamic limit, at low temperatures and small packing fractions, where clustering is favored and cluster-cluster interactions can be neglected, thermodynamically stable cluster phases can be formed. The analysis of the ground-state geometries shows that the spherical shape is marginally stable. In the majority of the studied cases, we find that above a certain size, ground-state clusters preferentially grow almost in one dimension.

Thermal aggregation of patatin studied in situ

In this work dynamic light scattering was used to study the thermal aggregation of patatin in situ, to elucidate the physical aggregation mechanism of the protein and to be able to relate the aggregation behavior to its structural properties. The dependence of the aggregation rates on the temperature and the ionic strength suggested a mechanism of slow coagulation, being both diffusion and chemically limited. The aggregation rate dependence on the protein concentration was in accordance with the mechanism proposed. The aggregation rates as obtained at temperatures ranging from 40 to 65 degrees C correlated well with unfolding of the protein at a secondary level. Small-angle neutron scattering and dynamic light scattering results were in good accordance; they revealed that native patatin has a cylindrical shape with a diameter and length of 5 and 9.8 nm, respectively.