Nanoparticles in solutions of adsorbing polymers: pair interactions, percolation, and phase behavior

We study the polymer adsorption characteristics, pair-interaction potentials, and phase and percolation behavior in nanoparticle-polymer mixtures. We propose a "saturable" adsorption model to capture the effect of the finite surface saturation capacity for adsorption, and use polymer self-consistent field theory in combination with a McMillan-Mayer framework [McMillan, W. G., Jr.; Mayer, J. E. J. Chem. Phys. 1945, 13, 276] to compute the pair-interaction potentials. Our results demonstrate novel size effects that distinguish the adsorption characteristics of nanoparticles from that of larger particles. Specifically, we predict that the nanoparticle regime is characterized by a significant adsorbance of polymers, albeit distributed predominantly in the form of tails. We also demonstrate that an interplay between the surface saturation, polymer-to-particle size ratios, and the polymer concentrations governs the overall effective interactions between nanoparticles in the presence of an adsorbing polymer. We use simple, mean-field models to relate these characteristics to the phase and percolation behavior in such systems. Our results show that the percolation thresholds for smaller particles are significantly smaller (and, overall, correspond only to a few volume percent) compared to that of the larger particles. Further, with a decrease in the size of the particles, we also predict a considerable increase in the miscibility of the polymer-particle mixtures. Our results are qualitatively in accord with many experimental observations in the nanoparticle regime.     

Effects of ammonium sulfate and sodium chloride concentration on PEG/protein liquid-liquid phase separation

When added to protein solutions, poly(ethylene glycol) (PEG) creates an effective attraction between protein molecules due to depletion forces. This effect has been widely used to crystallize proteins, and PEG is among the most successful crystallization agents in current use. However, PEG is almost always used in combination with a salt at either low or relatively high concentrations. Here the effects of sodium chloride and ammonium sulfate concentration on PEG 8000/ovalbumin liquid-liquid (L-L) phase separation are investigated. At low salt the L-L phase separation occurs at decreasing protein concentration with increasing salt concentration, presumably due to repulsive electrostatic interactions between proteins. At high salt concentration, the behavior depends on the nature of the salt. Sodium chloride has little effect on the L-L phase separation, but ammonium sulfate decreases the protein concentration at which the L-L phase separation occurs. This trend is attributed to the effects of critical fluctuations on depletion forces. The implications of these results for designing solution conditions optimal for protein crystallization are discussed.     

Interactions between colloidal particles induced by polymer brushes grafted onto the substrate

We investigate the interaction energy between two colloidal particles on or immersed in nonadsorbing polymer brushes grafted onto the substrate as a function of the separation of the particles by the use of a self-consistent-field theory calculation. Depending on the colloidal size and the penetration depth, we demonstrate the existence of a repulsive energy barrier of several kBT, which can be interpreted by separating the interaction energy into three parts: colloid-polymer interfacial energy, entropic contribution due to "depletion zone" overlap of colloidal particles, and entropic elastic energy of grafted chains by the compression of particles. The existence of a repulsive barrier which is of entirely entropic origin can lead to kinetic stabilization of the mixture rather than depletion flocculation or phase separation. Therefore, the present result may suggest an approach for controlling the self-assembling behavior of colloids for the formation of target structures, by tuning the colloidal interaction on the grafting substrate under appropriate selection of colloidal size, effective gravity (influencing the penetration depth), and brush coverage density.     

Protein Denaturation Through the Use of Magnetic Molecularly Imprinted Polymer Nanoparticles

The inhibition of the protein function for therapeutic applications remains challenging despite progress these past years. While the targeting application of molecularly imprinted polymer are in their infancy, no use was ever made of their magnetic hyperthermia properties to damage proteins when they are coupled to magnetic nanoparticles. Therefore, we have developed a facile and effective method to synthesize magnetic molecularly imprinted polymer nanoparticles using the green fluorescent protein (GFP) as the template, a bulk imprinting of proteins combined with a grafting approach onto maghemite nanoparticles. The hybrid material exhibits very high adsorption capacities and very strong affinity constants towards GFP. We show that the heat generated locally upon alternative magnetic field is responsible of the decrease of fluorescence intensity.     

On-chip solid phase extraction and enzyme digestion using cationic PolyE-323 coatings and porous polymer monoliths coupled to electrospray mass spectrometry

We evaluate the compatibility and performance of polymer monolith solid phase extraction beds that incorporate cationic charge, with a polycationic surface coating, PolyE-323, fabricated within microfluidic glass chips. The PolyE-323 is used to reduce protein and peptide adsorption on capillary walls during electrophoresis, and to create anodal flow for electrokinetically driven nano-electrospray ionization mass spectrometry. A hydrophobic butyl methacrylate-based monolithic porous polymer was copolymerized with an ionizable monomer, [2-(methacryloyloxy)ethyl] trimethylammonium chloride to form a polymer monolith for solid phase extraction that also sustains anodal electroosmotic flow. Exposure of the PolyE-323 coating to the monolith forming mixture affected the performance of the chip by a minor amount; electrokinetic migration times increased by ～5%, and plate numbers were reduced by an average of 5% for proteins and peptides. 1-mm long on-chip monolithic solid phase extraction columns showed reproducible, linear calibration curves (R(2)=0.9978) between 0.1 and 5 nM BODIPY at fixed preconcentration times, with a capacity of 2.4 pmol or 0.92 mmol/L of monolithic column for cytochrome c. Solution phase on-bed trypsin digestion was conducted by capturing model protein samples onto the monolithic polymer bed. Complete digestion of the proteins was recorded for a 30 min stop flow digestion, with high sequence coverage (88% for cytochrome c and 56% for BSA) and minimal trypsin autodigestion product. The polycationic coating and the polymer monolith materials proved to be compatible with each other, providing a high quality solid phase extraction bed and a robust coating to reduce protein adsorption and generate anodal flow, which is advantageous for electrospray.     

Multiphase coexistence in polydisperse colloidal mixtures

The authors study the phase behavior of mixtures of monodisperse colloidal spheres with a depletion agent which can have arbitrary shape and can possess a polydisperse size or shape distribution. In the low concentration limit considered here, the authors can employ the free-volume theory and take the geometry of particles of the depletion agent into account within the framework of fundamental measure theory. The authors apply their approach to study the phase diagram of a mixture of (monodisperse) colloidal spheres and two polydisperse polymer components. By fine tuning the distribution of the polymer, it is possible to construct a complex phase diagram which exhibits two stable critical points.     

Mixtures of charged colloid and neutral polymer: influence of electrostatic interactions on demixing and interfacial tension

The equilibrium phase behavior of a binary mixture of charged colloids and neutral, nonadsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with nonadditive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter-the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion concentration ratios, a free-volume approximation for the free energy is used to compute the fluid phase diagram, which describes demixing into colloid-rich (liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic interactions shifts the demixing binodal toward higher polymer concentration, stabilizing the mixture. The enhanced stability is attributed to a weakening of polymer depletion-induced attraction between electrostatically repelling macroions. Comparison with predictions of density-functional theory reveals a corresponding increase in the liquid-vapor interfacial tension. The predicted trends in phase stability are consistent with observed behavior of protein-polysaccharide mixtures in food colloids.     

Polymer-induced phase separation and crystallization in immunoglobulin G solutions

We study the effects of the size of polymer additives and ionic strength on the phase behavior of a nonglobular protein-immunoglobulin G (IgG)-by using a simple four-site model to mimic the shape of IgG. The interaction potential between the protein molecules consists of a Derjaguin-Landau-Verwey-Overbeek-type colloidal potential and an Asakura-Oosawa depletion potential arising from the addition of polymer. Liquid-liquid equilibria and fluid-solid equilibria are calculated by using the Gibbs ensemble Monte Carlo technique and the Gibbs-Duhem integration (GDI) method, respectively. Absolute Helmholtz energy is also calculated to get an initial coexisting point as required by GDI. The results reveal a nonmonotonic dependence of the critical polymer concentration rho(PEG) (*) (i.e., the minimum polymer concentration needed to induce liquid-liquid phase separation) on the polymer-to-protein size ratio q (equivalently, the range of the polymer-induced depletion interaction potential). We have developed a simple equation for estimating the minimum amount of polymer needed to induce the liquid-liquid phase separation and show that rho(PEG) (*) approximately [q(1+q)(3)]. The results also show that the liquid-liquid phase separation is metastable for low-molecular weight polymers (q=0.2) but stable at large molecular weights (q=1.0), thereby indicating that small sizes of polymer are required for protein crystallization. The simulation results provide practical guidelines for the selection of polymer size and ionic strength for protein phase separation and crystallization.     

Ligand-receptor interactions in tethered polymer layers

The binding of small proteins to ligands that are attached to the free ends of polymers tethered to a planar surface is studied using a molecular theory. The effects of changing the intrinsic binding equilibrium constant of the ligand-receptor pair, the polymer surface coverage, the polymer molecular weight, and the protein size are studied. The results are also compared with the case where ligands are directly attached to the surface without a polymer acting as a spacer. We found that within the biological range of binding constants the protein adsorption is enhanced by the presence of the polymer spacers. There is always an optimal surface coverage for which ligand-receptor binding is a maximum. This maximum increases as the binding energy and/or the polymer molecular weight increase. The presence of the maximum is due to the ability of the polymer-bound proteins to form a thick layer by dispersing the ligands in space to optimize binding and minimize lateral repulsions. The fraction of bound receptors is unity for a very small surface coverage of ligands. The very sharp decrease in the fraction of bound ligand-receptor pairs with surface coverage depends on the polymer spacer chain length. We found that the binding of proteins is reduced as the size of the protein increases. The orientation of the bound proteins can be manipulated by proper choice of the grafted layer conditions. At high polymer surface coverage the bound proteins are predominantly perpendicular to the surface, while at low surface coverage there is a more random distribution of orientations. To avoid nonspecific adsorption on the surface, we studied the case where the surface is covered by a mixture of a relatively high molecular weight polymer with a ligand attached to its free end and a low molecular weight polymer without ligand. These systems present a maximum in the binding of proteins, which is of the same magnitude as when only the long polymer-ligand is present. Moreover, when the total surface coverage in the mixed layers of polymers is high enough, nonspecific adsorption of the proteins on the surface is suppressed. The use of the presented theoretical results for the design of surface modifiers with tailored abilities for specific binding of proteins and optimal nonfouling capabilities is discussed.     

Accelerated SDS depletion from proteins by transmembrane electrophoresis: Impacts of Joule heating

SDS plays a key role in proteomics workflows, including protein extraction, solubilization and mass‐based separations (e.g. SDS‐PAGE, GELFrEE). However, SDS interferes with mass spectrometry and so it must be removed prior to analysis. We recently introduced an electrophoretic platform, termed transmembrane electrophoresis (TME), enabling extensive depletion of SDS from proteins in solution with exceptional protein yields. However, our prior TME runs required 1 h to complete, being limited by Joule heating which causes protein aggregation at higher operating currents. Here, we demonstrate effective strategies to maintain lower TME sample temperatures, permitting accelerated SDS depletion. Among these strategies, the use of a magnetic stir bar to continuously agitate a model protein system (BSA) allows SDS to be depleted below 100 ppm (>98% removal) within 10 min of TME operations, while maintaining exceptional protein recovery (>95%). Moreover, these modifications allow TME to operate without any user intervention, improving throughput and robustness of the approach. Through fits of our time‐course SDS depletion curves to an exponential model, we calculate SDS depletion half‐lives as low as 1.2 min. This promising electrophoretic platform should provide proteomics researchers with an effective purification strategy to enable MS characterization of SDS‐containing proteins.     

Quantitative analysis of two-dimensional gel-separated proteins using isotopically marked alkylating agents and matrix-assisted laser desorption/ionization mass spectrometry

We describe a simple approach for the relative quantification of individual proteins within a mixture. The method is based on the differential labelling of the mixtures by use of a commercially available acrylamide and deuterium-labelled [2,3,3'-d(3)]-acrylamide to alkylate proteins prior to two-dimensional (2-D) gel electrophoresis. The tryptic digests of the separated proteins were subjected to reflector matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) analysis and the relative peak heights of cysteine-containing peptides were used to quantify their precursor proteins. This approach was tested for the relative quantification of proteins within an artificial mixture of standard proteins and for proteins observed in a 2-D map of rat serum. A good correlation was found between the measured ratios derived from MALDI-TOF data and those theoretically calculated prior to 2-D analysis via known mixing ratios of the two alkylating reagents. The described procedure has proved to be effective for comparative measurements of protein abundances within the investigated mixtures.     

Preliminary assessment of the modification of polystyrene‐divinylbenzene resin with lipid‐tethered ligands for selective separations

Functionalized lipid tethered ligands use physical adsorption to anchor reactive head groups to hydrophobic supports. We previously demonstrated the use of these species adsorbed onto polypropylene capillary‐channeled polymer fibers. The general use of lipid tethered ligands on other hydrophobic chromatographic supports is demonstrated here for polystyrene‐divinylbenzene. Evaluation of ligand adsorption conditions was performed using a fluorescein isocyanate head group to quantify the extent of loading by UV‐Vis absorbance and by fluorescence microscopy. Selective protein capture was demonstrated by the detection of Texas Red labeled streptavidin (using fluorescence microscopy imaging, with quantification assessed through the depletion of solution‐phase protein using UV‐Vis absorbance. A second demonstration of the coupling involved an iminodiacetic acid head group lipid tethered ligand to capture the cationic dye, methylene blue. Two common means of alleviating nonspecific binding, adsorption in detergent media and use of a bovine serum albumin block, were evaluated. The first was found to cause release of the ligands, while the second was nominally effective. Indeed, the lipid tethered ligands itself may be most effective at impeding nonspecific binding. While further optimization and chromatographic evaluation is required, the general viability of this ligand immobilization method onto this common polymer support is demonstrated.     

Net charge and electrophoretic mobility of lysozyme charge ladders in solutions of nonionic surfactant

We report on the electrophoretic mobility and on the thermal diffusion of lysozyme proteins dissolved in aqueous solutions of a nonionic surfactant (C12E6) at a wide range of concentrations of the surfactant (0-20% by weight). We want to estimate the influence of a dense network of elongated micelles of C12E6 on the effective charge of the proteins as observed in the capillary electrophoresis experiments. The possible mechanism leading to the change in the effective charge of protein could involve the deformation of the cloud of counterions around the protein when it squeezes through the narrow (of the order of a protein diameter) aqueous channels formed in the solution of elongated micelles. The combination of independent measurements of the electrophoretic mobility of a family of modified proteins (lysozyme charge ladder [Colton et al. J. Am. Chem. Soc. 1997, 119, 12701]), of the microviscosity of the solutions of surfactant (obtained via fluorescence correlation spectroscopy), and of the hydrodynamic radius of the proteins (photon correlation spectroscopy) allow us to conclude that the effective charge of the proteins is not affected by the presence of surfactant, even at high concentrations.     

A novel method for the pore size control of the battery separator using the phase instability of the ternary mixtures

The battery separator plays a key role in determining the capacity of the battery. Since separator performance mainly depends on the pore size of membrane, development of a technique for the fabrication of the membrane having controlled pore size is essential in producing a highly functional battery separator. In this study, microporous membranes having the desired pore size were produced via thermally‐induced phase separation (TIPS) process. Control of the phase boundaries of polymer‐diluent blends is the main concern in manipulating pore size in TIPS process, because pore size mainly depends on the temperature gap between phase separation temperature of the blend and the crystallization temperature of polymer. Microporous membranes having controlled pore size were produced from polyethylene (PE)/dioctyl phthalate (DOP) blends, PE/isoparaffin blends, and polymer/diluent‐mixture ternary blends, that is, PE/(DOP/isoparaffin) blends. PE/DOP binary blends and PE/(DOP/isoparaffin) ternary blends exhibited typical upper critical solution temperature (UCST) type phase behavior, while PE formed a homogeneous mixture with isoparaffin above the crystallization temperature of PE. When the mixing ratio of polymer and diluent‐mixture was fixed, the phase separation temperature of PE/diluent‐mixture blend first increased with increasing DOP content in the diluent‐mixture, went through a maximum centered at about 80 wt % DOP and then decreased. Furthermore, the phase separation temperatures of the PE/diluent‐mixture blends were always higher than that of the PE/DOP blend when diluent‐mixture contained more than or equal to 20 wt % of DOP. Average pore size of microporous membrane prepared from PE/DOP blend and that prepared from PE/isoparaffin blend were 0.17 and 0.07 μm, respectively. However, average pore size of microporous membrane prepared from ternary blends was varied from 0.07 to 0.5 μm by controlling diluent mixing ratio. To understand the phase behavior of ternary blend, phase instability of the ternary mixture was also explored. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2025–2034, 2006     

Depletion induced isotropic-isotropic phase separation in suspensions of rod-like colloids

When non-adsorbing polymers are added to an isotropic suspension of rod-like colloids, the colloids effectively attract each other via depletion forces. We performed Monte Carlo simulations to study the phase diagram of such rod-polymer mixture. The colloidal rods were modeled as hard spherocylinders; the polymers were described as spheres of the same diameter as the rods. The polymers may overlap with no energy cost, while the overlap of polymers and rods is forbidden. Large amounts of depletant cause phase separation of the mixture. We estimated the phase boundaries of isotropic-isotropic coexistence both in the bulk and in confinement. To determine the phase boundaries we applied the grand canonical ensemble using successive umbrella sampling [J. Chem. Phys. 120, 10925 (2004)], and we performed a finite size scaling analysis to estimate the location of the critical point. The results are compared with predictions of the free volume theory developed by Lekkerkerker and Stroobants [Nuovo Cimento D 16, 949 (1994)]. We also give estimates for the interfacial tension between the coexisting isotropic phases and analyze its power-law behavior on the approach of the critical point.     

Controlled Supramolecular Self‐Assembly of Super‐charged β‐Lactoglobulin A–PEG Conjugates into Nanocapsules

The synthesis and characterization of a new protein–polymer conjugate composed of β lactoglobulin A (βLG A) and poly(ethylene glycol) PEG is described. βLG A was selectively modified to self‐assemble by super‐charging via amination or succinylation followed by conjugation with PEG. An equimolar mixture of the oppositely charged protein–polymer conjugates self‐assemble into spherical capsules of 80–100 nm in diameter. The self‐assembly proceeds by taking simultaneous advantage of the amphiphilicity and polyelectrolyte nature of the protein–polymer conjugate. These protein–polymer capsules or proteinosomes are reminiscent of protein capsids, and are capable of encapsulating solutes in their interior. We envisage this approach to be applicable to other globular proteins.     

Sedimentation of aggregating colloids

We investigate the combined effects of gravity, attractive interactions, and brownian motion in suspensions of colloidal particles and nonadsorbing polymer. Depending on the effective strength of gravitational forces, resulting from a density mismatch between the colloids and the solvent, and the magnitude and range of the depletion interactions induced by the polymer, sedimentation in these suspensions can result in an equilibrium structure or a kinetically arrested state. We employ large-scale molecular dynamics simulations to systematically classify the different regimes that arise as a function of attraction strength and gravitational stress. Whereas strong attractions lead to cluster aggregation and low-density arrested states, moderate attractions can enhance crystallization of the colloidal particles in the sediment. We make direct comparisons to experimental results to infer general conclusions about the mechanisms leading to mechanically stable sediments.     

Nylon-6 capillary-channeled polymer fibers as a stationary phase for the mixed-mode ion exchange/reversed-phase chromatography separation of proteins

Capillary-channeled polymer (C-CP) fibers extruded from nylon-6 are used as the stationary phase for the ion-exchange/reversed-phase mixed-mode chromatographic separation of a three protein mixture. The nylon-6 C-CP fibers are packed collinearly in a 250 x 1.5-mm i.d. column with an interstitial fraction of approximately 0.6. The effects of four displacing salts at three different pHs are studied with regards to protein retention time, peak width, selectivity, and resolution for a synthetic mixture consisting of myoglobin, ribonuclease A, and lysozyme to determine the optimum mobile phase conditions. The net charge model is found to be inadequate in fully explaining the retention behavior, as the proteins are retained by anion and cation-exchange interactions, as well as hydrophobic interactions with the stationary phase. It is found that pH and displacing salt strength had a significant influence on the retention properties and resolution of the proteins.     

Depletion-induced phase separation in colloid-polymer mixtures

Phase separation can be induced in a colloidal dispersion by adding non-adsorbing polymers. Depletion of polymer around the colloidal particles induces an effective attraction, leading to demixing at sufficient polymer concentration. This communication reviews theoretical and experimental work carried out on the polymer-mediated attraction between spherical colloids and the resulting phase separation of the polymer-colloid mixture. Theoretical studies have mainly focused on the limits where polymers are small or large as compared to the colloidal size. Recently, however, theories are being developed that cover a wider colloid-polymer size ratio range. In practical systems, size polydispersity and polyelectrolytes (instead of neutral polymers) and/or charges on the colloidal surfaces play a role in polymer-colloid mixtures. The limited amount of theoretical work performed on this is also discussed. Finally, an overview is given on experimental investigations with respect to phase behavior and results obtained with techniques enabling measurement of the depletion-induced interaction potential, the structure factor, the depletion layer thickness and the interfacial tension between the demixed phases of a colloid-polymer mixture.