Hydrodynamics and electrokinetics of spherical liposomes with coatings of terminally anchored poly(ethylene glycol): numerically exact electrokinetics with self-consistent mean-field polymer

Electric Fields at the Lipid Membrane Interface

This review presents a comprehensive analysis of electric field distribution at the water-lipid membrane interface in the context of its relationship to various biochemical problems. The main attention is paid to the methodological aspects of bioelectrochemical techniques and quantitative analysis of electrical phenomena caused by the ionization and hydration of the membrane-water interface associated with the phase state of lipids. One of the objectives is to show the unique possibility of controlling changes in the structure of the lipid bilayer initiated by various membrane-active agents that results in electrostatic phenomena at the surface of lipid models of biomembranes-liposomes, planar lipid bilayer membranes (BLMs) and monolayers. A set of complicated experimental facts revealed in different years is analyzed here in order of increasing complexity: from the adsorption of biologically significant inorganic ions and phase rearrangements in the presence of multivalent cations to the adsorption and incorporation of pharmacologically significant compounds into the lipid bilayer, and formation of the layers of macromolecules of different types.

Exploiting endocytosis for transfection of mRNA for cytoplasmatic delivery using cationic gold nanoparticles

Introduction

Gene therapy holds promise to cure various diseases at the fundamental level. For that, efficient carriers are needed for successful gene delivery. Synthetic 'non-viral' vectors, as cationic polymers, are quickly gaining popularity as efficient vectors for transmitting genes. However, they suffer from high toxicity associated with the permeation and poration of the cell membrane. This toxic aspect can be eliminated by nanoconjugation. Still, results suggest that optimising the oligonucleotide complexation, ultimately determined by the size and charge of the nanovector, is not the only barrier to efficient gene delivery.

Methods

We herein develop a comprehensive nanovector catalogue comprising different sizes of Au NPs functionalized with two different cationic molecules and further loaded with mRNA for its delivery inside the cell.

Results and Discussion

Tested nanovectors showed safe and sustained transfection efficiencies over 7 days, where 50 nm Au NPs displayed the highest transfection rates. Remarkably, protein expression was increased when nanovector transfection was performed combined with chloroquine. Cytotoxicity and risk assessment demonstrated that nanovectors are safe, ascribed to lesser cellular damage due to their internalization and delivery via endocytosis. Obtained results may pave the way to design advanced and efficient gene therapies for safely transferring oligonucleotides.

Non-monotonic variation of flow strength in nanochannels grafted with end-charged polyelectrolyte layers

The electrokinetic transport of fluids, also called the electroosmotic flow (EOF), in micro/nanoscale devices occurs in promising applications such as electrokinetic energy conversion (EKEC) systems. Recently, EKEC systems grafted with end-charged polyelectrolyte (PE) layers (PELs) have been reported to exhibit higher efficiencies than those of intrinsic systems. Understanding the interplay between the end-charged PELs and electrical double layers (EDLs) on the EOF is crucial for designing highly efficient EKEC systems. The interplay between the end-charged PELs and EDLs on the strength of the EOF (V₀) is studied by explicitly modeling the EOF through nanochannels grafted with end-charged PELs using atomic simulations. The variation of V₀ is examined for nanochannels grafted with PELs at various separations (d = 3.5–0.4 nm) to cover various conformations of PEs, inlcuding mushroom, semi-dilute brushes, and concentrated brushes. We find that V₀ follows a non-monotonic variation as d decreases and this is correlated with the conformation of the PEs. Specifically, as d decreases, V₀ decreases first in the mushroom regime (d = 3.5–2.0 nm), and then V₀ increases in the concentrated brush regime (d = 0.75–0.4 nm). Navigated by the continuum Navier–Stokes–Brinkman model, the above observations are rationalized by the competition between the driving effect from the spatial shift of ions in EDLs and the drag effect from PELs. The insights obtained in this work are important to guide the design of highly efficient EKEC systems by grafting end-charged PELs onto channel surfaces.

A non-monotonic variation of the strength of electroosmotic flow (V₀) is reported for the electroosmotic flow through nanochannels grafted with end-charged polyelectrolytes at various separation using atomic simulations.

Heterogeneity in Lateral Distribution of Polycations at the Surface of Lipid Membrane: From the Experimental Data to the Theoretical Model

Natural and synthetic polycations of different kinds attract substantial attention due to an increasing number of their applications in the biomedical industry and in pharmacology. The key characteristic determining the effectiveness of the majority of these applications is the number of macromolecules adsorbed on the surface of biological cells or their lipid models. Their study is complicated by a possible heterogeneity of polymer layer adsorbed on the membrane. Experimental methods reflecting the structure of the layer include the electrokinetic measurements in liposome suspension and the boundary potential of planar bilayer lipid membranes (BLM) and lipid monolayers with a mixed composition of lipids and the ionic media. In the review, we systematically analyze the methods of experimental registration and theoretical description of the laterally heterogeneous structures in the polymer layer published in the literature and in our previous studies. In particular, we consider a model based on classical theory of the electrical double layer, used to analyze the available data of the electrokinetic measurements in liposome suspension with polylysines of varying molecular mass. This model suggests a few parameters related to the heterogeneity of the polymer layer and allows determining the conditions for its appearance at the membrane surface. A further development of this theoretical approach is discussed.

Electrophoresis of soft particles with hydrophobic inner core grafted with pH-regulated and highly charged polyelectrolyte layer

Electrophoresis of core-shell composite soft particles possessing hydrophobic inner core grafted with highly charged polyelectrolyte layer (PEL) has been studied analytically. The PEL bears pH-dependent charge properties due to the presence of zwitterionic functional groups. The dielectric permittivity of the PEL and bulk aqueous medium were taken to be different, which resulted in the ion-partitioning effect. Objective of this study was to provide a simple expression for the mobility of such core-shell soft particles under Donnan limit where the thickness of the PEL well exceeds the electric double layer thickness. Going beyond the widely used Debye-Hückel linearization, the nonlinear Poisson-Boltzmann equation coupled with Stokes-Darcy-Brinkman equations was solved to determine the electrophoretic mobility. The derived expression further recovers all the existing results for the electrophoretic mobility under various simplified cases. The graphical presentation of the results illustrated the impact of pertinent parameters on the electrophoretic mobility of such a soft particle.

Spraying of Ultrathin Isoporous Block Copolymer Membranes-A Story about Challenges and Limitations

Isoporous membranes can be prepared by a combination of self-assembly of amphiphilic block copolymers and the non-solvent induced phase separation process. As the general doctor-blade technique suffers from high consumption of expensive block copolymer, other methods to reduce its concentration in the casting solution are sought after. Decreasing the block copolymer concentration during membrane casting and applying the block copolymer solution on a support membrane to obtain ultrathin isoporous membrane layers with e.g., spraying techniques, can be an answer. In this work we focused on the question if upscaling of thin block copolymer membranes produced by spraying techniques is feasible. To upscale the spray coating process, three different approaches were pursued, namely air-brush, 1-fluid nozzles and 2-fluid nozzles as generally used in the coating industry. The different spraying systems were implemented successfully in a membrane casting machine. Thinking about future development of isoporous block copolymer membranes in application it was significant that a continuous preparation process can be realised combining spraying of thin layers and immersion of the thin block copolymer layers in water to ensure phase-separation. The system was tested using a solution of polystyrene-block-poly(4-vinylpyridine) diblock copolymer. A detailed examination of the spray pattern and its homogeneity was carried out. The limitations of this method are discussed.

Electrophoresis of composite soft particles with differentiated core and shell permeabilities to ions and fluid flow

Within the framework of analytical theories for soft surface electrophoresis, soft particles are classically defined by a hard impermeable core of given surface charge density surrounded by a polyelectrolyte shell layer permeable to both electroosmotic flow and ions from background electrolyte. This definition excludes practical core-shell particles, e.g. dendrimers, viruses or multi-layered polymeric particles, defined by a polyelectrolytic core where structural charges are distributed and where counter-ions concentration and electroosmotic flow velocity can be significant. Whereas a number of important approximate expressions has been derived for the electrophoretic mobility of hard and soft particles, none of them is applicable to such generic composite core-shell particles with differentiated ions- and fluid flow-permeabilities of their core and shell components. In this work, we elaborate an original closed-form electrophoretic mobility expression for this generic composite particle type within the Debye-Hückel electrostatic framework and thin double layer approximation. The expression explicitly involves the screening Debye layer thickness and the Brinkman core and shell hydrodynamic length scales, which favors so-far missing analysis of the respective core and shell contributions to overall particle mobility. Limits of this expression successfully reproduce results from Ohshima's electrophoresis theory solely applicable to soft particles with or without hard core.

Hydrodynamic Properties of Polymers Screening the Electrokinetic Flow: Insights from a Computational Study

Understanding the hydrodynamic properties of polymeric coatings is crucial for the rational design of molecular transport involving polymeric surfaces and is relevant to drug delivery, sieving, molecular separations, etc. It has been found that the hydrodynamic radius of a polymer segment is an order of magnitude smaller than its physical size, but the origin of this effect does not seem to be well understood. Herein, we study the hydrodynamic properties of polymeric coatings by using molecular dynamics simulations, navigated by the continuous Navier-Stokes-Brinkman model. We confirm that the averaged hydrodynamic radius of a polymer bead is about one order of magnitude smaller than its physical radius, and, in addition, we show that it exhibits a strong dependence on the degree of polymerization. We relate this variation of the hydrodynamic radius to the structural properties and hydrodynamic shielding by surrounding polymer beads. This is done by separating the effects originating from near and far beads. For the near beads, shielding is mainly due to the two nearest beads (of the same polymer) and leads to about a 5-fold reduction in the hydrodynamic radius. Assuming the additivity of the hydrodynamic shielding by far beads, we suggest a simple model, which captures correctly the qualitative behaviour of the hydrodynamic radius with the degree of polymerization. The revealed shielding effects provide important insights relevant to the advanced modelling of hydrodynamic properties of polymeric coatings.

Size dependent targeted delivery of gold nanoparticles modified with the IL-6R-specific aptamer AIR-3A to IL-6R-carrying cells

The delivery of gold nanoparticles (AuNPs) to specific cells strongly depends on the properties e.g. the size of the particles and is of great interest for a large variety of biomedical applications. Here we investigated the size dependence of the receptor-ligand mediated AuNP delivery to cells by comparing very small "molecular" Au-clusters of only 2 nm to larger 7 nm and 36 nm AuNPs with a distinct surface plasmon resonance. Since the molecular weight in this range changes by almost three orders of magnitude, we show how the amount of gold relates to the number of delivered AuNPs. We attached small interleukin-6 receptor (IL-6R) specific aptamer molecules (AIR-3A) in different amounts to the particles and investigated the specificity of the delivery to IL-6R-carrying cells. To reduce unspecific interaction the particles were additionally covered with polyethylene glycol (PEG). Besides particle size and concentration we varied additional parameters such as aptamer surface coverage as well as incubation time and temperature. We found that in particular, small particles with diameters of less than 2 nm show an up to six times higher delivery rate for the aptamer-conjugated AuNPs compared to untargeted PEG-coated AuNPs. The specificity reduces with a decreasing aptamer/PEG ratio, and also with an increase in particle size where the unspecific uptake is much higher. In addition we also compared the delivery efficiency of this aptamer-mediated delivery system with an antibody-mediated system targeting the same receptor to validate the performance of this approach.

Quantifying the Sensitivity of Multipolar (Dipolar, Quadrupolar, and Octapolar) Surface Plasmon Resonances in Silver Nanoparticles: The Effect of Size, Composition, and Surface Coating

The effect of composition, size, and surface coating on the sensitivity of localized multipolar surface plasmon resonances has been spectroscopically investigated in high-quality silver colloidal solutions with precisely controlled sizes from 10 to 220 nm and well-defined surface chemistry. Surface plasmon resonance modes have been intensively characterized, identifying the size-dependence of dipolar, quadrupolar, and octapolar modes. Modifications of the NP's surface chemistry revealed the higher sensitivity of large sizes, long molecules, thiol groups, and low-order resonance modes. We also extend this study to gold nanoparticles, aiming to compare the sensitivity of both materials, quantifying the higher sensitivity of silver.

Thin Isoporous Block Copolymer Membranes: It Is All about the Process

The combination of the self-assembly of amphiphilic block copolymers and the nonsolvent induced phase inversion process offers an efficient way to isoporous integral-asymmetric membranes. In this context we report fast, easily upscalable and material reducing ways to thin self-assembled membranes. Therefore, we succeeded to implement a spray or dip coating step into the membrane formation process of different diblock copolymers like polystyrene-block-poly(4-vinylpyridine), poly(α-methylstyrene)-bock-poly(4-vinylpyridine), and polystyrene-block-poly(iso-propylglycidyl methacrylate). The formation of hexagonal pore structures was possible using a highly diluted one solvent system allowing the reduction of diblock copolymer consumption and therefore the production costs are minimized compared to conventional blade casting approaches. The broad applicability of the process was proven by using different flat and hollow fiber support materials. Furthermore, the membranes made by this new method showed a more than 6-fold increase in water flux compared to conventional polystyrene-block-poly(4-vinylpyridine) membranes with similar pore sizes prepared by blade casting. The membranes could be proven to be stable at transmembrane pressures of 2 bar and showed a pH responsive flux behavior over several cycles.

Electrophoretic Interpretation of PEGylated NP Structure with and without Peripheral Charge

Anchoring poly(ethylene glycol) (PEG) to inorganic nanoparticles (NPs) permits control over NP properties for a variety of technological applications. However, the core-shell structure tremendously complicates the interpretation of the ubiquitous ζ-potential, as furnished by electrophoretic light-scattering, capillary electrophoresis or gel electrophoresis. To advance the ζ-potential-and the more fundamental electrophoretic mobility-as a quantitative diagnostic for PEGylated NPs, we synthesized and characterized Au NPs bearing terminally anchored 5 kDa PEG ligands with univalent carboxymethyl end groups. Using the electrophoretic mobilities, acquired over a wide range of ionic strengths, we developed a theoretical model for the distributions of polymer segments, charge, electrostatic potential, and osmotic pressure that envelop the core: knowledge that will help to improve the performance of soft NPs in fundamental research and technological applications.

Neutron reflectometry elucidates density profiles of deuterated proteins adsorbed onto surfaces displaying poly(ethylene glycol) brushes: evidence for primary adsorption

The concentration profile of deuterated myoglobin (Mb) adsorbed onto polystyrene substrates displaying poly(ethylene glycol) (PEG) brushes is characterized by neutron reflectometry (NR). The method allows to directly distinguish among primary adsorption at the grafting surface, ternary adsorption within the brush, and secondary adsorption at the brush outer edge. It complements depth-insensitive standard techniques, such as ellipsometry, radioactive labeling, and quartz crystal microbalance. The study explores the effect of the PEG polymerization degree, N, and the grafting density, σ, on Mb adsorption. In the studied systems there is no indication of secondary or ternary adsorption, but there is evidence of primary adsorption involving a dense inner layer at the polystyrene surface. For sparsely grafted brushes the primary adsorption involves an additional dilute outer protein layer on top of the inner layer. The amount of protein adsorbed in the inner layer is independent of N but varies with σ, while for the outer layer it is correlated to the amount of grafted PEG and is thus sensitive to both N and σ. The use of deuterated proteins enhances the sensitivity of NR and enables monitoring exchange between deuterated and hydrogenated species.

Impact of electrostatics on the chemodynamics of highly charged metal-polymer nanoparticle complexes

In this work, the impact of electrostatics on the stability constant, the rate of association/dissociation, and the lability of complexes formed between Cd(II), Pb(II), and carboxyl-modified polymer nanoparticles (also known as latex particles) of radius ∼ 50 nm is systematically investigated via electroanalytical measurements over a wide range of pHs and NaNO3 electrolyte concentrations. The corresponding interfacial structure and key electrostatic properties of the particles are independently derived from their electrokinetic response, successfully interpreted using soft particle electrohydrodynamic formalism, and complemented by Förster resonance energy transfer (FRET) analysis. The results underpin the presence of an ∼0.7-1 nm thick permeable and highly charged shell layer at the surface of the polymer nanoparticles. Their electrophoretic mobility further exhibits a minimum versus NaNO3 concentration due to strong polarization of the electric double layer. Integrating these structural and electrostatic particle features with recent theory on chemodynamics of particulate metal complexes yields a remarkable recovery of the measured increase in complex stability with increasing pH and/or decreasing solution salinity. In the case of the strongly binding Pb(II), the discrepancy at pH > 5.5 is unambiguously assigned to the formation of multidendate complexes with carboxylate groups located in the particle shell. With increasing pH and/or decreasing electrolyte concentration, the theory further predicts a kinetically controlled formation of metal complexes and a dramatic loss of their lability (especially for lead) on the time-scale of diffusion toward a macroscopic reactive electrode surface. These theoretical findings are again shown to be in agreement with experimental evidence.

Electrophoretic mobility of sarcoplasmic reticulum vesicles - analytical model includes amino acid residues of A+P+N domain of Ca(2+)-ATPase and charged lipids

This work is an experimental and theoretical study of electrostatic and hydrodynamic properties of the surface of sarcoplasmic reticulum (SR) membrane using particle electrophoresis. The essential structural components of SR membrane include a lipid matrix and a dense layer of Ca(2+)-ATPases embedded in the matrix. The Ca(2+)-ATPase layer both drives and impedes vesicle mobility. To analyze the experimental mobility data, obtained at pH4.0, 4.7, 5.0, 6.0, 7.5, and 9.0 in 0.1M monovalent (1:1) electrolyte, an analytical solution for the vesicle mobility and electroosmotic flow velocity distribution was obtained by solving the Poisson-Boltzmann and the Navier-Stokes-Brinkman equations. The electrophoretic mobility model includes two sets of charges that represent: (a) charged lipids of the lipid matrix of the vesicle core, and (b) charged amino acid residues of APN domains of Ca(2+)-ATPases. APN domains are assumed to form a charged plane displaced from the surface of lipid matrix. The charged plane is embedded in a frictional layer that represents the surface layer of calcium pumps. Electrophoretic mobility is driven by the charged APN domain and by lipid matrix while the surface layer provides hydrodynamic friction. The charge of APN domain is determined by ionized amino acid residues obtained from the amino acid composition of SERCA1a Ca(2+)-ATPase. Agreement between the measured and the predicted mobility is evaluated by the weighted sum of mobility deviation squared. This model reproduces the experimental dependence of mobility on pH and predicts that APN domains are located in the upper half of the SR vesicle surface layer.

Self-consistent colloidal energy and diffusivity landscapes in macromolecular solutions

We report a dynamic analysis to simultaneously measure colloidal forces and hydrodynamic interactions in the presence of both adsorbed and unadsorbed macromolecules. A Bayesian inference method is used to self-consistently obtain the position-dependent potential energy (i.e., energy landscape) and diffusivity (i.e., diffusivity landscape) from measured colloidal trajectories normal to a wall. Measurements are performed for particles and surfaces with adsorbed polyethylene oxide (PEO) copolymer as a function of unadsorbed PEO homopolymer concentration. Energy landscapes are well described by a steric repulsion between adsorbed brushes and depletion attraction due to unadsorbed macromolecules. Diffusivity landscapes show agreement with predicted short-range permeable brush models and long-range mobilities determined by the bulk solution viscosity. Lower than expected mobilities in the vicinity of overlapping depletion layers are attributed to interactions of adsorbed and unadsorbed macromolecules altering nonconservative lubrication forces.

Effect of the spacer structure on the stability of gold nanoparticles functionalized with monodentate thiolated poly(ethylene glycol) ligands

Poly(ethylene glycol)- (PEG-) based ligands are well-established for the stabilization of nanoparticles in aqueous solution and are especially interesting for applications in medicine and biotechnology because they are known to improve the pharmacokinetic properties of nanomaterials. In this study, we prepared gold nanoparticles (AuNPs) with ligand shells of different monodentate poly(ethylene glycol)-thiol (PEG-SH) ligands. These ligands differed only in the segment connecting the thiol group with the PEG moiety (Mw ≈ 2000 g/mol) through an ester bond, the spacer. All ligands were synthesized by straightforward esterification. Specifically, we used PEG ligands with a long (C10, PEGMUA) or short (C2, PEGMPA) alkylene spacer or a phenylene (PEGMPAA) spacer. The influence of the spacer on the stability of gold nanoparticle-PEG conjugates (AuNP@PEG) was tested by cyanide etching experiments, electrolyte-induced aggregation, and competitive ligand displacement with dithiothreitol (DTT). In the presence of 100 mM cyanide, AuNPs stabilized with PEGMPA or PEGMPAA were completely dissolved by oxidative etching within a few minutes, whereas AuNPs stabilized with PEGMUA needed more than 20 h to be completely etched. By complementary experiments, we deduced a simplified description for the etching process that takes into account the role of excess ligand. In the presence of free ligand, significantly fewer AuNPs are etched, suggesting a competition of etching and ligand binding to AuNPs. We also compared the stabilizing effect of PEGMUA with that of a bidentate PEG-thiol ligand (PEGLIP) and found a reversed stability against cyanide etching and DTT displacement, in agreement with previously reported observations. Our results clearly demonstrate the strong impact of the spacer structure on conjugate stability and provide valuable information for the rational design of more complex AuNP@PEG conjugates, which are of much interest in the context of biotechnology and medical applications.

Macro- versus microscopic view on the electrokinetics of a water-membrane interface

Electrophoresis is an experimental method widely used to study electrostatic properties of interfaces. Here, we question the validity of the macroscopic theory for the planar geometry by Helmholtz and Smoluchowski by considering a POPC bilayer in an aqueous solution with 500 mM NaCl, using molecular dynamics simulations. We find that POPC shows positive electrophoretic mobility due to adsorption of sodium ions at the lipid headgroups. The theory assumes that the region in which the water density undergoes a transition from the bulk value to zero (interfacial width) is small compared to the Debye screening length. This separation of length scale is not fullfilled in the present case. Hence, contrasting the theory, we observe that the surface is not sharply defined, continuum hydrodynamics is not applicable, the effective viscosity in the double layer is increased compared to the bulk, and the zeta potential is dominated by the dipole potential. Our results might have widespread implications for interpretation of electrokinetic studies in general.

Polarization of a diffuse soft particle subjected to an alternating current field

The polarization of a diffuse soft particle submerged in an aqueous electrolyte and subjected to a uniform alternating electric field is theoretically analyzed with the standard electrokinetic model (the Poisson-Nernst-Planck equations). The particle consists of a rigid uncharged core and a charged diffuse polyelectrolytic shell (soft layer) permeable to ions and solvent. Our focus is on the impact of the characteristics of the soft layer including the Donnan potential, the soft layer thickness, and the friction coefficient of the soft layer on the dipole coefficient, characterizing the strength of the polarization. Under the limits of thin double layers and thin polyelectrolytic shells, approximate analytical expressions to evaluate the dipole moment coefficients are derived for high-frequency and low-frequency ranges, respectively. The analytical results are compared and agree favorably with those numerically computed by the standard model. Interestingly, we discover that when the double layer is comparable to the soft layer the dipole moment behaves qualitatively differently at different Donnan potentials. When the Donnan potential is small, the dipole moment decreases as the double layer increases. In contrast, at large Donnan potentials, the dipole moment increases with the increase in the double layer. The distinct responses to Donnan potentials are attributed to the impact of the associated double layer on the charge distribution of mobile ions inside the soft layer. The theoretical model provides a fundamental basis for interpreting the polarization of heterogeneous systems, including environmental or biological colloids or microgel particles.

Nanoparticle ζ -potentials

For over half a century, alternating electric fields have been used to induce particle transport, furnishing the ζ-potential of analytes with sizes ranging from a few nanometers to several micrometers. Concurrent advances in nanotechnology have provided new materials for catalysis, self-assembly, and biomedical applications, all of which benefit from a thorough understanding of particle surface charge. Therefore, the measurement of the ζ-potential via electrophoretic light scattering (ELS) has become essential for nanoparticle (NP) research. However, the interpretation of NP electrophoretic mobility, especially that of ligand-coated NPs, can be a complex undertaking. Despite the inherent intricacy of these data, key concepts from colloidal science can help to distill valuable information from ELS. In this Account, we adopt PEGylated Au NPs as an illustrative example to explore extensions of the classical theories of Smoluchowski, Hückel, and Henry to more contemporary theories for ligand-coated NP systems such as those from Ohshima, and Hill, Saville, and Russel. First, we review the basic experimental considerations necessary to understand NP electrophoretic mobility, identifying when O'Brien and White's numerical solution of the standard electrokinetic model should be adopted over Henry's closed-form analytical approximation. Next, we explore recent developments in the theory of ligand-coated particle electrophoresis, and how one can furnish accurate and meaningful relationships between measured NP mobility, ζ-potential, and surface charge. By identifying key ligand-coated NP parameters (e.g., coating thickness, permeability, molecular mass, and hydrodynamic segment size), we present a systematic method for quantitatively interpreting NP electrophoretic mobility. In addition to reviewing theoretical foundations, we describe our recent results that examine how the unique surface curvature of NPs alters and controls their properties. These data provide guidelines that can expedite the rational design of NPs for advanced uses, such as heterogeneous catalysis and in vivo drug delivery. As a practical demonstration of these concepts, we apply the ligand-coated theory to a recently developed noncovalent PEGylated Au NP drug-delivery system. Our analysis suggests that anion adsorption on the Au NP core may enhance the stability of these NP-drug conjugates in solution. In addition to providing useful nanochemistry insights, the information in this Account will be useful to biomedical and materials engineers, who use ELS and ζ-potentials for understanding NP dynamics.

Study of PEGylated lipid layers as a model for PEGylated liposome surfaces: molecular dynamics simulation and Langmuir monolayer studies

We have combined Langmuir monolayer film experiments and all-atom molecular dynamics (MD) simulation of a bilayer to study the surface structure of a PEGylated liposome and its interaction with the ionic environment present under physiological conditions. Lipids that form both gel and liquid-crystalline membranes have been used in our study. By varying the salt concentration in the Langmuir film experiment and including salt at the physiological level in the simulation, we have studied the effect of salt ions present in the blood plasma on the structure of the poly(ethylene glycol) (PEG) layer. We have also studied the interaction between the PEG layer and the lipid bilayer in both the liquid-crystalline and gel states. The MD simulation shows two clear results: (a) The Na(+) ions form close interactions with the PEG oxygens, with the PEG chains forming loops around them and (b) PEG penetrates the lipid core of the membrane for the case of a liquid-crystalline membrane but is excluded from the tighter structure of the gel membrane. The Langmuir monolayer results indicate that the salt concentration affects the PEGylated lipid system, and these results can be interpreted in a fashion that is in agreement with the results of our MD simulation. We conclude that the currently accepted picture of the PEG surface layer acting as a generic neutral hydrophilic polymer entirely outside the membrane, with its effect explained through steric interactions, is not sufficient. The phenomena we have observed may affect both the interaction between the liposome and bloodstream proteins and the liquid-crystalline-gel transition and is thus relevant to nanotechnological drug delivery device design.

Electrophoretic characterization of insulin growth factor (IGF-1) functionalized magnetic nanoparticles

The synthesis of composite nanoparticles consisting of a magnetite core coated with a layer of the hormone insulin growth factor 1 (IGF-1) is described. The adsorption of the hormone in the different formulations is first studied by electrophoretic mobility measurements as a function of pH, ionic strength, and time. Because of the permeable character expected for both citrate and IGF-1 coatings surrounding the magnetite cores, an appropriate analysis of their electrophoretic mobility must be addressed. Recent developments of electrokinetic theories for particles covered by soft surface layers have rendered possible the evaluation of the softness degree from raw electrophoretic mobility data. In the present contribution, the data are quantitatively analyzed based on the theoretical model of the electrokinetics of soft particles. As a result, information is obtained on both the thickness and the charge density of the surrounding layer. It is shown that IGF-1 adsorbs onto the surface of citrate-coated magnetite nanoparticles, and adsorption is confirmed by dot-blot analysis. In addition, it is also demonstrated that the external layer of IGF-1 exerts a shielding effect on the surface charge of citrate-magnetite particles, as suggested by the mobility reduction upon contacting the particles with the hormone. Aging effects are demonstrated, providing an electrokinetic fingerprint of changes in adsorbed protein configuration with time.

Electrophoretic mobilities of PEGylated gold NPs

Electromigration of nanoparticles (NPs) is relevant to many technological and biological applications. We correlate the experimentally observed electromigration of Au NPs with a closed-form theoretical model that furnishes key NP characteristics, including the previously unknown values of Au NP core ζ-potential, PEG-corona permeability, and particle-hydrogel friction coefficient. More generally, the theory furnishes new understanding of NP electromigration in complex environments, establishing a robust and predictive model to guide the design and characterization of functionalized NPs.

Polymer adsorption onto a micro-sphere from optical tweezers electrophoresis

We explore the design and operation of an optical-tweezers electrophoresis apparatus to resolve polymer adsorption dynamics onto a single micro-sphere in a micro-fluidic environment. Our model system represents a broader class of micro-fluidic electrophoresis experiments for biosensing and fundamental colloid and surface science diagnostics. We track the adsorption of 100 kDa poly(ethylene oxide) homopolymer onto a colloidal silica sphere that is optically trapped in a crossed parallel-plate micro-channel. The adsorption dynamics are probed on the ∼1 μm particle length scale with ∼1 s temporal resolution. Because the particle electrophoretic mobility and channel electro-osmotic flow are exquisitely sensitive to the polymer layer hydrodynamic thickness, particle dynamics can be complicated by polymer adsorption onto the micro-channel walls. Nevertheless, using experiments and a theoretical model of electro-osmotic flow in channels with non-uniform wall ζ-potentials, we show that such influences can be mitigated by adopting a symmetrical flow configuration. The equilibrium hydrodynamic layer thickness of 100 kDa poly(ethylene oxide) on colloidal silica is ∼10 nm at polymer concentrations ≳10 ppm (weight percent), with the dynamics reflecting polymer solution concentration, flow rate, and polydispersity.

Lipopolymer gradient diffusion in supported bilayer membranes

We measure the gradient diffusion coefficient of a model lipopolymer in supported lipid bilayer membranes from Fourier-transform post-electrophoresis relaxation. The experiments and accompanying quantitative interpretation furnish the concentration dependence of the gradient diffusion coefficient. In striking contrast to the recent measurements of the self-diffusion coefficient from fluorescence recovery after photobleaching, the lipopolymer gradient diffusion coefficient increases with concentration. We interpret the enhancement at small but finite concentrations using the Scalettar-Abney-Owicki (SAO) statistical mechanical theory (1988) and the Bussell-Koch-Hammer (BKH) hydrodynamic theory (1995), which are customarily adopted to model membrane protein dynamics. The SAO theory furnishes an effective disc radius and soft repulsive interaction radius that are comparable to the Flory radius of the unperturbed polyethylene glycol chains. On the other hand, the BKH theory predicts a gradient diffusion coefficient that decreases with disc/membrane protein concentration. Thus, in contrast to membrane proteins, we conclude that lipopolymer hydrodynamic interactions are weak because the principal disturbances are in the low-viscosity aqueous phase. Accordingly, lipopolymer interactions are dominated by thermodynamic interactions among polymer chains. Interestingly, our experiments suggest that increasing (decreasing) the polymer molecular weight should increase (decrease) the relaxation rate of lipopolymer concentration fluctuations.

Competitive adsorption of thiolated polyethylene glycol and mercaptopropionic acid on gold nanoparticles measured by physical characterization methods

Competitive adsorption kinetics between thiolated polyethylene glycol (SH-PEG) and mercaptopropionic acid (MPA) on gold nanoparticles (Au-NPs) were studied using a prototype physical characterization approach that combines dynamic light scattering (DLS) and electrospray differential mobility analysis (ES-DMA). The change in hydrodynamic particle size (intensity average) due to the formation of SH-PEG coatings on Au-NPs was measured by DLS in both two-component (Au-NP + MPA or Au-NP + SH-PEG) and three-component (Au-NP +MPA + SH-PEG) systems. ES-DMA was employed to quantify the surface coverage of SH-PEG and establish a correlation between surface coverage and the change in particle size measured by DLS. A change in the equilibrium binding constant for SH-PEG on Au-NPs at various concentrations of SH-PEG and MPA showed that the presence of MPA reduced the binding affinity of SH-PEG to the Au-NP surface. Kinetic studies showed that SH-PEG was desorbed from the Au-NP surface following a second-order desorption model after subsequently introducing MPA. The desorption rate constant of SH-PEG from the Au-NP surface by MPA displacement was strongly affected by the concentration of MPA and the excess SH-PEG in solution.

Theory of electrostatics and electrokinetics of soft particles

We investigate theoretically the electrostatics and electrokinetics of a soft particle, i.e. a hard particle covered with an ion-penetrable surface layer of polyelectrolytes. The electric properties of soft particles in an electrolyte solution, which differ from those of hard particles, are essentially determined by the Donnan potential in the surface layer. In particular, the Donnan potential plays an essential role in the electrostatics and electrokinetics of soft particles. Furthermore, the concept of zeta potential, which is important in the electrokinetics of hard particles, loses its physical meaning in the electrokinetics of soft particles. In this review, we discuss the potential distribution around a soft particle, the electrostatic interaction between two soft particles, and the motion of a soft particle in an electric field.

A phenomenological one-parameter equation of state for osmotic pressures of PEG and other neutral flexible polymers in good solvents

We present a phenomenological one-parameter scaling equation of state that accurately represents osmotic pressures of neutral flexible polymers in good solvents from the dilute through the semidilute regime. The equation comprises a sum of scaled van't Hoff and des Cloizeaux terms including a fitted parameter alpha, the "crossover index", which encapsulates all chemical specificity and determines the relevant prefactors. Strikingly different values of alpha are found for the two very different systems poly(ethyleneglycol)/water (PEG) and poly(alpha-methylstyrene)/toluene (PAMS). Alpha-dependent rescaling collapses both data sets to a simple one-parameter scaling function. The fact that the anomalous system PEG/water and the canonical system PAMS/toluene can both be described by the same equation of state attests to the robustness of the polymer-scaling concepts introduced by de Gennes.

Primary electroviscous effect in a dilute suspension of soft particles

A theory for the primary electroviscous effect in a dilute suspension of soft particles (i.e., particles coated with an ion-penetrable surface layer of polyelectrolytes) in an electrolyte solution is presented. The general expression for the effective viscosity eta s of the suspension and the primary electroviscous coefficient p, which is further expressed in terms of a function L, is given. On the basis of the general expressions, we derive approximate analytic expressions for eta s and p, which are applicable when the density of the fixed charges distributed within the surface layer is low. Further we obtain a simple approximate analytic expression (without involving numerical integrations) for p applicable for most practical cases. It is found that the function L exhibits a minimum when plotted as a function of kappa a (kappa is the Debye-Hückel parameter and a is the particle core radius), unlike the case of a suspension of hard particles, in which case L decreases as kappa a increases, exhibiting no minimum. The presence of a minimum for the case of a suspension of soft particles is due to the fact that L is proportional to 1/kappa 2 at small kappa a and to kappa 2 at large kappa a. Because of the presence of this minimum, the difference in L between soft and hard particles becomes very large for large kappa a.

Impact of chemical and structural anisotropy on the electrophoretic mobility of spherical soft multilayer particles: the case of bacteriophage MS2

We report a theoretical investigation of the electrohydrodynamic properties of spherical soft particles composed of permeable concentric layers that differ in thickness, soft material density, chemical composition, and flow penetration degree. Starting from a recent numerical scheme developed for the computation of the direct-current electrophoretic mobility (mu) of diffuse soft bioparticles, the dependence of mu on the electrolyte concentration and solution pH is evaluated taking the known three-layered structure of bacteriophage MS2 as a supporting model system (bulk RNA, RNA-protein bound layer, and coat protein). The electrokinetic results are discussed for various layer thicknesses, hydrodynamic flow penetration degrees, and chemical compositions, and are discussed on the basis of the equilibrium electrostatic potential and hydrodynamic flow field profiles that develop within and around the structured particle. This study allows for identifying the cases where the electrophoretic mobility is a function of the inner structural and chemical specificity of the particle and not only of its outer surface properties. Along these lines, we demonstrate the general inapplicability of the notions of zeta potential (zeta) and surface charge for quantitatively interpreting electrokinetic data collected for such systems. We further shed some light on the physical meaning of the isoelectric point. In particular, numerical and analytical simulations performed on structured soft layers in indifferent electrolytic solution demonstrate that the isoelectric point is a complex ionic strength-dependent signature of the flow permeation properties and of the chemical and structural details of the particle. Finally, the electrophoretic mobilities of the MS2 virus measured at various ionic strength levels and pH values are interpreted on the basis of the theoretical formalism aforementioned. It is shown that the electrokinetic features of MS2 are to a large extent determined not only by the external proteic capsid but also by the chemical composition and hydrodynamic flow permeation of/within the inner RNA-protein bound layer and bulk RNA part of the bacteriophage. The impact of virus aggregation, as revealed by decreasing diffusion coefficients for decreasing pH values, is also discussed.

Hard versus soft particle electrokinetics of silica colloids

To verify the existence of a gel layer at the surface of silica, dependences of the electrophoretic mobility of fresh and aged colloidal silica particles on the KCl concentration are measured. These dependences, corrected for the relaxation/polarization effect, are fitted by analytical expressions based on the model of hard, soft, and brush surfaces. A bad fit is obtained for both silicas when its surface is considered ideal (hard). Much better fits are achieved with the invariable soft layer model for the fresh silica but especially for the aged silica whose surface is less charged probably as a result of an extension and/or loosening of the layer. A perfect fit is found for aged silica when applying a trivial model of the soft polyelectrolyte layer combined with the scaling model of polyelectrolyte brushes.

Electrophoresis of diffuse soft particles

A theory is presented for the electrophoresis of diffuse soft particles in a steady dc electric field. The particles investigated consist of an uncharged impenetrable core and a charged diffuse polyelectrolytic shell, which is to some extent permeable to ions and solvent molecules. The diffuse character of the shell is defined by a gradual distribution of the density of polymer segments in the interspatial region separating the core from the bulk electrolyte solution. The hydrodynamic impact of the polymer chains on the electrophoretic motion of the particle is accounted for by a distribution of Stokes resistance centers. The numerical treatment of the electrostatics includes the possibility of partial dissociation of the hydrodynamically immobile ionogenic groups distributed throughout the shell as well as specific interaction between those sites with ions from the background electrolyte other than charge-determining ions. Electrophoretic mobilities are computed on the basis of an original numerical scheme allowing rigorous evaluation of the governing transport and electrostatic equations derived following the strategy reported by Ohshima, albeit within the restricted context of a discontinuous chain distribution. Attention is particularly paid to the influence of the type of distribution adopted on the electrophoretic mobility of the particle as a function of its size, charge, degree of permeability, and solution composition. The results are systematically compared with those obtained with a discontinuous representation of the interface. The theory constitutes a basis for interpreting electrophoretic mobilities of heterogeneous systems such as environmental or biological colloids or swollen/deswollen microgel particles.

Transport in polymer-gel composites: Response to a bulk concentration gradient

This paper examines the response of electrolyte-saturated polymer gels, embedded with charged spherical inclusions, to a weak gradient of electrolyte concentration. An electrokinetic model was presented in an earlier publication, and the response of homogeneous composites to a weak electric field was calculated. In this work, the influence of the inclusions on bulk ion fluxes and the strength of an electric field (or membrane diffusion potential) induced by the bulk electrolyte concentration gradient are computed. Effective ion diffusion coefficients are significantly altered by the inclusions, so-depending on the inclusion surface charge or zeta potential-asymmetric electrolytes can behave as symmetrical electrolytes and vice versa. The theory also quantifies the strength of flow driven by concentration-gradient-induced perturbations to the equilibrium diffuse double layers. Similarly to diffusiophoresis, the flow may be either up or down the applied concentration gradient.

Covalently anchored lipid structures on amine-enriched polystyrene

The study of the adhesion of lipid vesicles on surfaces is of increasing interest in the field of medical implants and tissue engineering (protein-resistant surfaces), drug delivery, biosensors, and biochips. In this work, lipid coverage was developed from PEG-coated vesicles (with sizes from 100 to 300 nm) by covalently binding poly(ethylene glycol)-alpha-disteroylphosphatidylethanolamine-omega-benzotriazole carbonate (DSPE-PEG-BTC) molecules onto the surface amine groups by carbamate chemistry. Lipid surface density and the surface structure of multilamellar (MLVs) and extruded unilamellar (LUVs) vesicles deposited on three types of polystyrene (PS) well-plates were probed by fluorescence and atomic force microscopy (AFM) imaging. A significant difference in the vesicle surface coverage of PS substrates was observed with a substantial increase in lipid multilayers on the amine-enriched PS surface using both unilamellar and multilamellar vesicles.