The role of salt–macroion van der Waals interactions in the colloid–colloid potential of mean force

Maintained particulate integrity of soy protein nanoparticles during gastrointestinal digestion via genipin crosslinking enhancing stability and bioavailability of curcumin

Poor stability during gastrointestinal digestion is a major challenge for the applications of protein-based nanoparticles as oral delivery systems. In this work, genipin was used to crosslink the partially enzymatic hydrolyzed soy protein nanoparticles, aiming to improve their performance in gastrointestinal tract as delivery carrier. Results showed that the obtained genipin-crosslinked soy protein nanoparticles (GSPNPs) were still spherically monodisperse with a diameter around 60 nm. Encapsulation with GSPNPs significantly improved the solubility of curcumin (Cur) and its stability against UV light as well as long-term storage. Compared to those un-crosslinked nanoparticles, particles crosslinked by genipin had a more compact structure less sensitive to ionic effect and digestive enzymes, showing enhanced digestion stability. The well-maintained nanoparticulate structure of GSPNPs further contributed to the enhanced bioaccessibility and facilitated absorption by epithelial cells. Furthermore, in vivo experiment on rats showed that Cur encapsulated in GSPNPs exhibited a slowed down and sustained absorption manner with an 8.11-fold improvement in its bioavailability. These suggested that GSPNPs could be a promising nanocarrier to enhance the bioavailability of functional factors.

Protein Association in Solution: Statistical Mechanical Modeling

Protein molecules associate in solution, often in clusters beyond pairwise, leading to liquid phase separations and high viscosities. It is often impractical to study these multi-protein systems by atomistic computer simulations, particularly in multi-component solvents. Instead, their forces and states can be studied by liquid state statistical mechanics. However, past such approaches, such as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, were limited to modeling proteins as spheres, and contained no microscopic structure-property relations. Recently, this limitation has been partly overcome by bringing the powerful Wertheim theory of associating molecules to bear on protein association equilibria. Here, we review these developments.

Crystalline restacking of 2D-materials from their nanosheets suspensions

We report here the highly ordered restacking of the layered phosphatoantimonic dielectric materials H3(1-x)M3xSb3P2O14, (where M = Li, Na, K, Rb, Cs and 0 ≤ x ≤ 1), from their nanosheets dispersed in colloidal suspension, induced by a simple pH change using alkaline bases. H3Sb3P2O14 aqueous suspensions are some of the rare examples of colloidal suspensions based on 2D materials exhibiting a lamellar liquid crystalline phase. Because the lamellar period can reach several hundred nanometers, the suspensions show vivid structural colors and because these colors are sensitive to various chemicals, the suspensions can be used as sensors. The structures of the lamellar liquid crystalline phase and the restacked phase have been studied by X-ray scattering (small and wide angle), which has followed the dependence of the lamellar/restacked phase equilibrium on the cation exchange rate, x. The X-ray diffraction pattern of the restacked phase is almost identical to that of the M3Sb3P2O14 crystalline phase, showing that the restacking is highly accurate and avoids the turbostratic disorder of the nanosheets classically observed in nanosheet stacking of other 2D materials. Strikingly, the restacking process exhibits features highly reminiscent of a first-order phase transition, with the existence of a phase coexistence region where both ∼1 nm (interlayer spacing of the restacked phase) and ∼120 nm lamellar periods can be observed simultaneously. Furthermore, this first-order phase transition is well described theoretically by incorporating a Lennard-Jones-type lamellar interaction potential into an entropy-based statistical physics model of the lamellar phase of nanosheets. Our work shows that the precise cation exchange produced at room temperature by a classical neutralization reaction using alkaline bases leads to a crystal-like restacking of the exfoliated free Sb3P2O143- nanosheets from suspension, avoiding the turbostratic disorder typical of van der Waals 2D materials, which is detrimental to the controlled deposition of nanosheets into complex integrated electronic, spintronic, photonic or quantum structures.

Image-charge effects on ion adsorption near aqueous interfaces

Electrostatic interactions near surfaces and interfaces are ubiquitous in many fields of science. Continuum electrostatics predicts that ions will be attracted to conducting electrodes but repelled by surfaces with lower dielectric constant than the solvent. However, several recent studies found that certain "chaotropic" ions have similar adsorption behavior at air/water and graphene/water interfaces. Here we systematically study the effect of polarization of the surface, the solvent, and solutes on the adsorption of ions onto the electrode surfaces using molecular dynamics simulation. An efficient method is developed to treat an electrolyte system between two parallel conducting surfaces by exploiting the mirror-expanded symmetry of the exact image-charge solution. With neutral surfaces, the image interactions induced by the solvent dipoles and ions largely cancel each other, resulting in no significant net differences in the ion adsorption profile regardless of the surface polarity. Under an external electric field, the adsorption of ions is strongly affected by the surface polarization, such that the charge separation across the electrolyte and the capacitance of the cell is greatly enhanced with a conducting surface over a low-dielectric-constant surface. While the extent of ion adsorption is highly dependent on the electrolyte model (the polarizability of solvent and solutes, as well as the van der Waals radii), we find the effect of surface polarization on ion adsorption is consistent throughout different electrolyte models.

Controlling the viscosities of antibody solutions through control of their binding sites

For biotechnological drugs, it is desirable to formulate antibody solutions with low viscosities. We go beyond previous colloid theories in treating protein-protein self-association of molecules that are antibody-shaped and flexible and have spatially specific binding sites. We consider interactions either through fragment antigen (Fab-Fab) or fragment crystalizable (Fab-Fc) binding. Wertheim's theory is adapted to compute the cluster-size distributions, viscosities, second virial coefficients, and Huggins coefficients, as functions of antibody concentration. We find that the aggregation properties of concentrated solutions can be anticipated from simpler-to-measure dilute solutions. A principal finding is that aggregation is controllable, in principle, through modifying the antibody itself, and not just the solution it is dissolved in. In particular: (i) monospecific antibodies having two identical Fab arms can form linear chains with intermediate viscosities. (ii) Bispecific antibodies having different Fab arms can, in some cases, only dimerize, having low viscosities. (iii) Arm-to-Fc binding allows for three binding partners, leading to networks and high viscosities.

Explicit-water theory for the salt-specific effects and Hofmeister series in protein solutions

Effects of addition of salts on stability of aqueous protein solutions are studied theoretically and the results are compared with experimental data. In our approach, all the interacting species, proteins, ions, and water molecules, are accounted for explicitly. Water molecules are modeled as hard spheres with four off-center attractive square-well sites. These sites serve to bind either another water or to solvate the ions or protein charges. The ions are represented as charged hard spheres, and decorated by attractive sites to allow solvation. Spherical proteins simultaneously possess positive and negative groups, represented by charged hard spheres, attached to the surface of the protein. The attractive square-well sites, mimicking the protein-protein van der Waals interaction, are located on the surface of the protein. To obtain numerical results, we utilized the energy route of Wertheim's associative mean spherical approximation. From measurable properties, we choose to calculate the second virial coefficient B2, which is closely related to the tendency of proteins to aggregate and eventually crystalize. Calculations are in agreement with experimental trends: (i) For low concentration of added salt, the alkali halide salts follow the inverse Hofmeister series. (ii) At higher concentration of added salt, the trend is reversed. (iii) When cations are varied, the salts follow the direct Hofmeister series. (iv) In contrast to the colloidal theories, our approach correctly predicts the non-monotonic behavior of B2 upon addition of salts. (v) With respect to anions, the theory predicts for the B2 values to follow different sequences below and above the iso-ionic point, as also confirmed experimentally. (vi) A semi-quantitative agreement between measured and calculated values for the second virial coefficient, as functions of pH of solution and added salt type and concentration, is obtained.

Inhomogeneous screening near the dielectric interface

Screening is one of the most important concepts in the study of charged systems. Near a dielectric interface, the ion distribution in a salt solution can be highly nonuniform. Here, we develop a theory that self-consistently treats the inhomogeneous screening effects. At higher concentrations when the bulk Debye screening length is comparable to the Bjerrum length, the double layer structure and interfacial properties are significantly affected by the inhomogeneous screening. In particular, the depletion zone is considerably wider than that predicted by the bulk screening approximation or the WKB approximation. The characteristic length of the depletion layer in this regime scales with the Bjerrum length, resulting in a linear increase of the negative adsorption of ions with concentration, in agreement with experiments. For asymmetric salts, inhomogeneous screening leads to enhanced charge separation and surface potential.

Anisotropic protein-protein interactions due to ion binding

Self-association of proteins is strongly affected by long-range electrostatic interactions caused by equilibrium adsorption of small ions such as protons and multivalent metals. By affecting the molecular net charge, solution pH is thus a widely used parameter to tune stability and phase behavior of proteins. We here review recent studies where the charge distribution is perturbed not only by protons, but also by other binding ions, leading to a rich and inherently anisotropic charge distribution. Focus is on coarse grained simulation techniques, coupled to experiments of protein-protein interaction at varying salt and pH conditions. Finally, and with future bio-colloidal models in mind, we discuss the validity of coarse graining charge anisotropy using electric multipoles.

Protein aggregation in salt solutions

Protein aggregation is broadly important in diseases and in formulations of biological drugs. Here, we develop a theoretical model for reversible protein-protein aggregation in salt solutions. We treat proteins as hard spheres having square-well-energy binding sites, using Wertheim's thermodynamic perturbation theory. The necessary condition required for such modeling to be realistic is that proteins in solution during the experiment remain in their compact form. Within this limitation our model gives accurate liquid-liquid coexistence curves for lysozyme and γ IIIa-crystallin solutions in respective buffers. It provides good fits to the cloud-point curves of lysozyme in buffer-salt mixtures as a function of the type and concentration of salt. It than predicts full coexistence curves, osmotic compressibilities, and second virial coefficients under such conditions. This treatment may also be relevant to protein crystallization.

Specific ion effects on the self-assembly of ionic surfactants: a molecular thermodynamic theory of micellization with dispersion forces

The self-assembly of amphiphilic molecules is a key process in numerous biological and chemical systems. When salts are present, the formation and properties of molecular aggregates can be altered dramatically by the specific types of ions in the electrolyte solution. We present a molecular thermodynamic model for the micellization of ionic surfactants that incorporates quantum dispersion forces to account for specific ion effects explicitly through ionic polarizabilities and sizes. We assume that counterions are distributed in the diffuse region according to a modified Poisson-Boltzmann equation and can reach all the way to the micelle surface of charge. Stern layers of steric exclusion or distances of closest approach are not imposed externally; these are accounted for through the counterion radial distribution profiles due to the incorporation of dispersion potentials, resulting in a simple and straightforward treatment. There are no adjustable or fitted parameters in the model, which allows for a priori quantitative prediction of surfactant aggregation behavior based only on the initial composition of the system and the surfactant molecular structure. The theory is validated by accurately predicting the critical micelle concentration (CMC) for the well-studied sodium dodecyl sulfate (SDS) surfactant and its alkaline-counterion derivatives in mono- and divalent salts, as well as the molecular structure parameters of SDS micelles such as aggregation numbers and micelle surface potential.

Continuous self-energy of ions at the dielectric interface

By treating both the short-range (solvation) and long-range (image force) electrostatic forces as well as charge polarization induced by these forces in a consistent manner, we obtain a simple theory for the self-energy of an ion that is continuous across the interface. Along with nonelectrostatic contributions, our theory enables a unified description of ions on both sides of the interface. Using intrinsic parameters of the ions, we predict the specific ion effect on the interfacial affinity of halogen anions at the water-air interface, and the strong adsorption of hydrophobic ions at the water-oil interface, in agreement with experiments and atomistic simulations.

The stabilities of protein crystals

We describe a model for protein crystallization equilibria. The model includes four terms, (1) protein translational entropy opposes crystallization, (2) proteins are attracted to each other by a nonelectrostatic contact free energy favoring crystallization, (3) proteins in the crystal repel each other but, to a greater extent, attract counterions sequestered in the crystal, which favors crystallization, and (4) the translational entropy of the counterions opposes their sequestration into the crystal, opposing crystallization. We treat the electrostatics using the nonlinear Poisson-Boltzmann equation, and we use unit cell information from native protein crystals to determine the boundary conditions. This model predicts the stabilities of protein crystals as functions of temperature, pH, and salt concentrations, in good agreement with the data of Pusey et al. on tetragonal and orthorhombic crystal forms of lysozyme. The experiments show a weak dependence of crystal solubility on pH. According to the model, this is because the entropic cost to neutralize the crystal is compensated by favorable protein-salt interactions. Experiments also show that adding salt stabilizes the crystal. Cohn's empirical law predicts that the logarithm of solubility should be a linear function of salt. The present theory predicts nonlinearity, in better agreement with the experiments. The model shows that the salting out phenomena is not due to more counterion shielding but to lowered counterion translational entropy. Models of this type may help guide faster and better ways to crystallize proteins.

Ion-specific thermodynamical properties of aqueous proteins

Ion-specific interactions between two colloidal particles are calculated using a modified Poisson-Boltzmann (PB) equation and Monte Carlo (MC)simulations. PB equations present good results of ionic concentration profiles around a macroion, especially for salt solutions containing monovalent ions. These equations include not only electrostatic interactions, but also dispersion potentials originated from polarizabilities of ions and proteins. This enables us to predict ion-specific properties of colloidal systems. We compared results obtained from the modified PB equation with those from MC simulations and integral equations. Phase diagrams and osmotic second virial coefficients are also presented for different salt solutions at different pH and ionic strengths, in agreement with the experimental results observed Hofmeister effects. In order to include the water structure and hydration effect, we have used an effective interaction obtained from molecular dynamics of each ion and a hydrophobic surface combined with PB equation. The method has been proved to be efficient and suitable for describing phenomena where the water structure close to the interface plays an essential role. Important thermodynamic properties related to protein aggregation, essential in biotechnology and pharmaceutical industries, can be obtained from the method shown here.

Ion specific protein assembly and hydrophobic surface forces

Large anions are attracted to hydrophobic surfaces while smaller, well solvated ions are repelled. Using a combination of explicit solvent and continuum model simulations we show that this leads to significant ion-specific protein-protein interactions due to hydrophobic patches on the protein surfaces. In solutions of NaI and NaCl we calculate the potentials of mean force and find that the resulting second virial coefficients for lysozyme correspond well with experiment. We argue that ionic interactions with nonpolar surface groups may play an important role for biomolecular assembly and Hofmeister-type effects.

Specific ion binding to macromolecules: effects of hydrophobicity and ion pairing

Using molecular dynamics simulations in an explicit aqueous solvent, we examine the binding of fluoride versus iodide to a spherical macromolecule with both hydrophobic and positively charged patches. Rationalizing our observations, we divide the ion association interaction into two mechanisms: (1) poorly solvated iodide ions are attracted to hydrophobic surface patches, while (2) the strongly solvated fluoride and to a minor extent also iodide bind via cation-anion interactions. Quantitatively, the binding affinities vary significantly with the accessibility of the charged groups as well as the surface potential; therefore, we expect the ion-macromolecule association to be modulated by the local surface characteristics of the (bio-)macromolecule. The observed cation-anion pairing preference is in excellent agreement with experimental data.

Field theory for size- and charge-asymmetric primitive model of ionic systems: mean-field stability analysis and pretransitional effects

The primitive model of ionic systems is investigated within a field-theoretic description for the whole range of diameter-, lambda , and charge, Z ratios of the two ionic species. Two order parameters (OP) are identified. The relation of the OP's to physically relevant quantities is nontrivial. Each OP is a linear combination of the charge density and the number-density waves. Instabilities of the disordered phase associated with the two OP's are determined in the mean-field approximation (MF). In MF a gas-liquid separation occurs for any Z and lambda is not equal to 1 . In addition, an instability with respect to various types of periodic ordering of the two kinds of ions is found. Depending on lambda and Z , one or the other transition is metastable in different thermodynamic states. For sufficiently large size disparity we find a sequence of fluid-crystal-fluid transitions for the increasing volume fraction of ions, in agreement with experimental observations. The instabilities found in MF represent weak ordering of the most probable instantaneous states, and are identified with structural loci associated with pretransitional effects.

Analysis of osmotic pressure data for aqueous protein solutions via a multicomponent model

Integral equation theories and Monte Carlo simulations were used to study the Donnan equilibrium, which is established by an equilibrium distribution of a simple electrolyte between an aqueous protein-electrolyte mixture and an aqueous solution of the same simple electrolyte, when these two phases are separated by a semipermeable membrane. In order to describe the unusually low osmotic pressure found in many experiments we assumed that protein molecules can form dimers. The model solution contains proteins in a monomeric form, represented as charged hard spheres, or in a dimerized form, modeled as fused charged hard spheres. The counterions and coions were also modeled as charged hard spheres but of a much smaller size. The associative mean spherical and hypernetted-chain approximations were applied to this model. In addition, Monte Carlo computer simulations were performed for the same model system mimicking a lysozyme solution in the presence of 0.1 M sodium chloride. Theory and simulations were found to be in reasonably good agreement for the thermodynamic properties such as chemical potential and osmotic pressure under these conditions. Using the theoretical approaches mentioned above, we analyzed the experimental data for the osmotic pressure of bovine serum albumin in 0.15 M sodium chloride, human serum albumin solution (HSA) in 0.1 M phosphate buffer, and lysozyme in sulphate and phosphate buffers. The theoretically determined osmotic coefficients were fitted to the existing experimental data in order to obtain the fraction of dimers in solution. Our analysis indicated that there was relatively small self-association of protein molecules for bovine serum albumin solutions at pH=5.4 and 7.3, with the fraction of dimers smaller than 10%, while at pH=4.5 the dimer fraction was equal to 50%. In the case of HSA solutions, strong negative deviations from the ideal value were found and at pH=8.0 a reasonably good agreement between the theory and experiment is obtained by assuming full dimerization. For HSA solution at pH=5.4, the best fit to the experimental results was obtained for a fraction of dimers equal to 80%.