Phase behavior of mixtures of oppositely charged protein nanoparticles at asymmetric charge ratios

Colloidal Clusters and Networks Formed by Oppositely Charged Nanoparticles with Varying Stiffnesses

Colloidal clusters and gels are ubiquitous in science and technology. Particle softness has a strong effect on interparticle interactions; however, our understanding of the role of this factor in the formation of colloidal clusters and gels is only beginning to evolve. Here, we report the results of experimental and simulation studies of the impact of particle softness on the assembly of clusters and networks from mixtures of oppositely charged polymer nanoparticles (NPs). Experiments were performed below or above the polymer glass transition temperature, at which the interaction potential and adhesive forces between the NPs were significantly varied. Hard NPs assembled in fractal clusters that subsequently organized in a kinetically arrested colloidal gel, while soft NPs formed dense precipitating aggregates, due to the NP deformation and the decreased interparticle distance. Importantly, interactions of hard and soft NPs led to the formation of discrete precipitating NP aggregates at a relatively low volume fraction of soft NPs. A phenomenological model was developed for interactions of oppositely charged NPs with varying softnesses. The experimental results were in agreement with molecular dynamics simulations based on the model. This work provides insight on interparticle interactions before, during, and after the formation of hard-hard, hard-soft, and soft-soft contacts and has impact for numerous applications of reversible colloidal gels, including their use as inks for additive manufacturing.

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.

Charge-regulation phase transition on surface lattices of titratable sites adjacent to electrolyte solutions: An analog of the Ising antiferromagnet in a magnetic field

We report a charge-patterning phase transition on two-dimensional square lattices of titratable sites, here regarded as protonation sites, placed in a low-dielectric medium just below the planar interface between this medium and a salt solution. We calculate the work-of-charging matrix of the lattice with use of a linear Debye-Hückel model, as input to a grand-canonical partition function for the distribution of occupancy patterns. For a large range of parameter values, this model exhibits an approximate inverse cubic power-law decrease of the voltage produced by an individual charge, as a function of its in-lattice separation from neighboring titratable sites. Thus, the charge coupling voltage biases the local probabilities of proton binding as a function of the occupancy of sites for many neighbors beyond the nearest ones. We find that even in the presence of these longer-range interactions, the site couplings give rise to a phase transition in which the site occupancies exhibit an alternating, checkerboard pattern that is an analog of antiferromagnetic ordering. The overall strength W of this canonical charge coupling voltage, per unit charge, is a function of the Debye length, the charge depth, the Bjerrum length, and the dielectric coefficients of the medium and the solvent. The alternating occupancy transition occurs above a curve of thermodynamic critical points in the (pH-pK,W) plane, the curve representing a charge-regulation analog of variation of the Néel temperature of an Ising antiferromagnet as a function of an applied, uniform magnetic field. The analog of a uniform magnetic field in the antiferromagnet problem is a combination of pH-pK and W, and 1/W is the analog of the temperature in the antiferromagnet problem. We use Monte Carlo simulations to study the occupancy patterns of the titratable sites, including interactions out to the 37th nearest-neighbor category (a distance of √74 lattice constants), first validating simulations through comparison with exact and approximate results for the nearest-neighbor case. We then use the simulations to map the charge-patterning phase boundary in the (pH-pK,W) plane. The physical parameters that determine W provide a framework for identifying and designing real surfaces that could exhibit charge-patterning phase transitions.

Anisotropic Interactions in Protein Mixtures: Self Assembly and Phase Behavior in Aqueous Solution

Recent experimental studies show that oppositely charged proteins can self-assemble to form seemingly stable microspheres in aqueous salt solutions. We here use parallel tempering Monte Carlo simulations to study protein phase separation of lysozyme/α-lactalbumin mixtures and show that anisotropic electrostatic interactions are important for driving protein self-assembly. In both dilute and concentrated protein phases, the proteins strongly align according to their charge distribution. While this alignment can be greatly diminished by a single point mutation, phase separation is completely suppressed when neglecting electrostatic anisotropy. The results highlight the importance of subtle electrostatic interactions even in crowded biomolecular environments where other short-ranged forces are often thought to dominate.

Influence of architecture on the interaction of negatively charged multisensitive poly(N-isopropylacrylamide)-co-methacrylic acid microgels with oppositely charged polyelectrolyte: absorption vs adsorption

Two sets of core-shell microgels composed of temperature-sensitive poly(N-isopropylacrylamide) (PNiPAM) with different spatial distribution of pH-sensitive methacrylic acid (MAA) groups were prepared. The cores consist of either PNiPAM (neutral core; nc) or PNiPAM-co-MAA (charged core; cc). A charged shell existing of PNiPAM-co-MAA was added to the neutral core (yielding neutral core-charged shell; nccs), on the charged core, on the other hand, a neutral shell of PNiPAM was added (charged core-neutral shell; ccns). Complexes of these microgels with positively charged poly(diallyldimethylammonium chloride) (PDADMAC) of different molar masses were prepared. The amount of bound polyelectrolyte was quantified, and the microgel-polyelectrolyte complexes were characterized with respect to electrophoretic mobility and hydrodynamic radius. The penetration of polyelectrolyte into the microgel was also monitored by means of lifetime analysis of a fluorescent dye covalently bound to poly(L-lysine) providing information on the probe's local environment. The architecture of the microgel has a significant influence on the interaction with oppositely charged polyelectrolyte. Complexes with microgel with the charged shell tend to flocculate at charge ratios of 1 and are thus similar to polyelectrolyte complexes with rigid colloidal particles. Complexes with microgels that consist of a charged core and a neutral shell show very different properties: They are still temperature sensitive and reveal an influence of the polyelectrolyte's chain length. Low molecular weight PDADMAC can penetrate through the neutral shell into the charged core, and thus nearly no charge reversal occurs. The high-MW polyelectrolyte does not penetrate fully and leads to charge reversal. The results demonstrate that microgels are able to absorb or adsorb polyelectrolytes depending on the polyelectrolyte's chain length and the microgels architecture. Complexes with different surface properties and different colloidal stability can be prepared, and polyelectrolytes can be encapsulated in the microgel core. Thus, multisensitive core-shell microgels combine permeability and compartmentalization on a nanometer length scale and provide unique opportunities for applications in controlled uptake and release.

Adsorption of the protein bovine serum albumin in a planar poly(acrylic acid) brush layer as measured by optical reflectometry

The adsorption of bovine serum albumin (BSA) in a planar poly(acrylic acid) (PAA) brush layer has been studied by fixed-angle optical reflectometry. The influence of polymer length, grafting density, and salt concentration is studied as a function of pH. The results are compared with predictions of an analytical polyelectrolyte brush model, which incorporates charge regulation and excluded volume interactions. A maximum in adsorption is found near the point of zero charge (pzc) of the protein. At the maximum, BSA accumulates in a PAA brush to at least 30 vol %. Substantial adsorption continues above the pzc, that is, in the pH range where a net negatively charged protein adsorbs into a negatively charged brush layer, up to a critical pH value. This critical pH value decreases with increasing ionic strength. The adsorbed amount increases strongly with both increasing PAA chain length and increasing grafting density. Experimental data compare well with the analytical model without having to include a nonhomogeneous charge distribution on the protein surface. Instead, charge regulation, which implies that the protein adjusts its charge due to the negative electrostatic potential in the brush, plays an important role in the interpretation of the adsorbed amounts. Together with nonelectrostatic interactions, it explains the significant protein adsorption above the pzc.

Toward the description of electrostatic interactions between globular proteins: Potential of mean force in the primitive model

Monte Carlo simulations are used to calculate the exact potential of mean force between charged globular proteins in aqueous solution. The aim of the present paper is to study the influence of the ions of the added salt on the effective interaction between these nanoparticles. The charges of the model proteins, either identical or opposite, are either central or distributed on a discrete pattern. Contrarily to Poisson-Boltzmann predictions, attractive, and repulsive direct forces between proteins are not screened similarly. Moreover, it has been shown that the relative orientations of the charge patterns strongly influence salt-mediated interactions. More precisely, for short distances between the proteins, ions enhance the difference of the effective forces between (i) like-charged and oppositely charged proteins, (ii) attractive and repulsive relative orientations of the proteins, which may affect the selectivity of protein/protein recognition. Finally, such results observed with the simplest models are applied to a more elaborate one to demonstrate their generality.