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.     

Electrokinetic phenomena of soft particles

A review is given on the recent developments of theories of electrokinetics of soft particles (i.e., hard particles covered with an ion-penetrable surface layer of polyelectrolytes) with particular emphasis on the electrophoretic relaxation effects for highly charged soft particles and the effects of inhomogeneous distribution of polymer segments in the surface layer. The electrostatic interaction between soft particles is also discussed. Not only the interaction before contact of the surface layers of the interacting particles but also the interaction after their contact is considered.     

Nonlinear electrophoresis of dielectric particles in Newtonian fluids

In classical electrokinetics, the electrophoretic velocity of a dielectric particle is a linear function of the applied electric field. Theoretical studies have predicted the onset of nonlinear electrophoresis at high electric fields because of the nonuniform surface conduction over the curved particle. However, experimental studies have been left behind and are insufficient for a fundamental understanding of the parametric effects on nonlinear electrophoresis. We present in this work a systematic experimental study of the effects of buffer concentration, particle size, and particle zeta potential on the electrophoretic velocity of polystyrene particles in a straight rectangular microchannel for electric fields of up to 3 kV/cm. The measured nonlinear electrophoretic particle velocity is found to exhibit a 2(±0.5)-order dependence on the applied electric field, which appears to be within the theoretically predicted 3- and 3/2-order dependences for low and high electric fields, respectively. Moreover, the obtained nonlinear electrophoretic particle mobility increases with decreasing buffer concentration (for the same particle) and particle size (for particles with similar zeta potentials) or increasing particle zeta potential (for particles with similar sizes). These observations are all consistent with the theoretical predictions for high electric fields.     

Progress in electrohydrodynamics of soft microbial particle interphases

Electrokinetic phenomena, such as electrophoresis, are valuable tools for determining the interfacial (double layer) properties of colloidal particles. The theoretical formalisms employed to interpret electrokinetic data (electrophoretic mobility) were initially derived for the restrictive case of hard (non-permeable) particles with the electrokinetic potential as unavoidable primary variable. In this paper, we underline the inadequacy of such models for addressing the electrostatic and hydrodynamic characteristics of microbes like bacteria, viruses or yeast cells. These bioparticles are characterized by heterogeneous, soft, permeable interphases formed with the outer electrolytic medium, which requires advanced electrokinetic analyses where the concept of zeta-potential must be abandoned. We review the progresses made in the measurement and analysis of interphasial properties of bioparticles under electrokinetic conditions. In particular, emphasis is given on the necessity to couple appropriately interpreted electrokinetics with other physico-chemical measurements (e.g. issued from AFM imaging/force spectroscopy) and microbiological techniques (genetic manipulation of microbes). Using such a combination, a clear connection between complex interphase properties of microbes and e.g. their propensity to adhere onto charged surfaces should be achieved.     

The Effect of Protein Concentration on Electrophoretic Mobility

A theory of sedimentation in a concentrated suspension of spherical soft particles (i.e., polyelectrolyte-coated particles) is developed to obtain general expressions for sedimentation velocity of soft particles and sedimentation potential in the suspension. An Onsager relation between sedimentation potential and electrophoretic mobility of spherical soft particles in concentrated suspensions is derived for the case of low potentials and nonoverlapping electrical double layers of adjacent particles. Copyright 2000 Academic Press.     

Electrophoresis of soft particles: analytic approximations

An approximate analytic expression is derived for the electrophoretic mobility of a weakly charged spherical soft particle (i.e., a hard particle covered with a weakly charged polyelectrolyte layer) on the basis of the general mobility expression for soft particles (Ohshima, H., J. Colloid Interface Sci. 2000, 228, 190-193). The obtained mobility expression, which reproduces various approximate results so far derived and gives some new mobility formulas, covers all types of weakly charged soft particles with arbitrary values of the thickness of polymer layer, the radius of the particle core, the electrophoretic softness, and the Debye length, including spherical polyelectrolytes with no particle core as well as spherical hard particles with no polyelectrolyte layer.     

Effects of dielectric gradients-mediated ions partitioning on the electrophoresis of composite soft particles: An analytical theory

In this work, we report original analytical expressions defining the electrophoretic mobility of composite soft particles comprising an inner core and a surrounding polymer shell with differentiated permeabilities to ions from aqueous background electrolyte and to fluid flow developed under applied DC field conditions. The existence of dielectric permittivity gradients operational at the core/shell and shell/solution interfaces is accounted for within the Debye–Hückel approximation and flat plate configuration valid in the thin double layer regime. The proposed electrophoretic mobility expressions, applicable to weakly to moderately charged particles with size well exceeding the Debye layer thickness, involve the relevant parameters describing the particle core/shell structure and the electrohydrodynamic features of the core and shell particle components. It is shown that the analytical expressions reported so far in literature for the mobility of hard (impermeable) or porous particles correspond to asymptotic limits of the more generic results detailed here. The impacts of dielectric-mediated effects of ions partitioning between bulk solution and particle body on the electrophoretic response are further discussed. The obtained expressions pave the way for a refined quantitative, analytical interpretation of electrophoretic mobility data collected on soft (nano)particles (e.g., functionalized dendrimers and multilayered polyelectrolytic particles) or biological cells (e.g., viruses) for which the classical hard core-soft shell representation is not appropriate.     

Electrophoresis of soft particles at high electrolyte concentrations: an interpretation by the Henry theory

The existence of electrophoretic mobility at high electrolyte concentrations defines a remarkable peculiarity in the electrosurface characteristics of soft particles. According to Ohshima [H. Ohshima, Colloids Surf. 103 (1995) 249], this effect is caused by the electroosmotic flow within the soft particle shell. An explanation supporting Ohshima's conclusion can be derived from classic electrokinetic theories. Based on the Henry theory [D.C. Henry, Proc. R. Soc. London Ser. A 133 (1931) 106], we demonstrate that the electrophoretic mobility of soft particles does not disappear at decinormal concentration.     

Electrokinetics of soft polymeric interphases with layered distribution of anionic and cationic charges

Soft surface coatings attract increasing attention due to the versatile options they provide in numerous applications e.g. in the flourishing nanomedicine and nanobiotechnology areas. Optimisation of the performance of such ion- and solvent-permeable polyelectrolytic materials requires a detailed understanding of their electrostatic properties. This task is rendered difficult by the inherent non-uniform distribution of their structural charges. In this article, we review recent advances made in the measurement and theory of the electrokinetics (electrophoresis/streaming current) of soft surface coatings that carry spatially-separated cationic and anionic charges. Examples of such charge-stratified systems are polyelectrolyte-coated particles, polyelectrolyte multilayers, particles with zwitterionic interfacial functionality, microbial cells or hard–soft composite interfaces. It is shown here that the electrokinetic features of such colloidal systems are remarkably different from those of their counterparts with homogeneously distributed cationic and anionic charges. In particular, the interplay between electrostatic and hydrodynamic flow fields developed under electrokinetic conditions in the bulk and interfacial compartments of charge-stratified colloids/films are shown to induce a reversal of their electrokinetic response (electrophoretic mobility/streaming current) that depends on the concentration of monovalent electrolyte in solution. The prerequisites for occurrence of such spectacular behaviour are theoretically identified in terms of the Debye length, the spatial length scales defining charge layering, and the typical length for flow penetration within the colloids/films. Electrophoresis and streaming current results recently reported for poly(amidoamine) carboxylated nanodendrimers, natural rubber colloids and poly(ethyleneimine)-supported lipid bilayers are further discussed to illustrate the generic electrokinetic properties of soft interfaces defined by a given stratification of their anionic and cationic structural charges.     

Approximate analytic expressions for the electrophoretic mobility of spheroidal particles

Approximate analytic expressions are derived for the electrophoretic mobility of spheroidal particles (prolate and oblate) carrying low zeta potential in an electrolyte solution under an applied tangential or transverse electric field. The present approximation method, which is based on the observation that the electrophoretic mobility of a particle is determined mainly by the distortion of the applied electric field by the presence of the particle. The exact expression for the equilibrium electric potential distribution around the particle, which can be expressed as an infinite sum of spheroidal wave functions, is not needed in the present approximation. The electrophoretic mobility values calculated with these approximate expressions for spheroidal particles with constant surface potential or constant surface charge density are in excellent agreement with the exact numerical results of previous reports with the relative errors less than about 4%.     

Electrophoretic mobility, zeta potential, and fixed charge density of bovine knee chondrocytes, methyl methacrylate-sulfopropyl methacrylate, polybutylcyanoacrylate, and solid lipid nanoparticles

The electrophoretic mobility and zeta potential of bovine knee chondrocytes (BKCs), methyl methacrylate-sulfopropyl methacrylate (MMA-SPM) nanoparticles (NPs), polybutylcyanoacrylate (PBCA) NPs, and solid lipid nanoparticles (SLNs) were investigated under the influences of Na+, K+, and Ca2+ with various ionic strengths. The fixed charge density in the surface layers of the four biocolloidal particles was estimated from the experimental mobility of capillary electrophoresis with a theory of soft charged colloids. The results revealed that, for a specific cationic species, the absolute values of the electrophoretic mobility, the zeta potential, and the fixed charge density decreased with an increase in ionic strength. For a constant ionic strength, the effect of ionic species on the reduction in the absolute values of the electrophoretic mobility, the zeta potential, and the fixed charge density followed the order Na+>K+>Ca2+ for the negatively charged BKCs, MMA-SPM NPs, and SLNs. The reverse order is true for the positively charged PBCA NPs.     

Relevance of electrokinetic theory for "soft" particles to bacterial cells: implications for bacterial adhesion

Bacterial cells and other biological particles carry charged macromolecules on their surface that form a "soft" ion-permeable layer. In this paper, we test the applicability of an electrokinetic theory for soft particles to characterize the electrophoretic mobility (EPM) and adhesion kinetics of bacterial cells. The theory allows the calculation of two parameters--the electrophoretic softness and the fixed charged density--that define the characteristics of the polyelectrolyte layer at the soft particle surface. The theory also allows the calculation of an outer-surface potential that may better predict the electrostatic interaction of soft particles with solid surfaces. To verify its relevance for bacterial cells, the theory was applied to EPM measurements of two well-characterized Escherichia coli K12 mutants having lipopolysaccharide (LPS) layers of different lengths and molecular compositions. Results showed that the obtained softness and fixed charge density were not directly related to the known characteristics of the LPS of the selected strains. Interaction energy profiles calculated from Derjaguin-Landau-Verwey-Overbeek (DLVO) theory were used to interpret bacterial deposition (adhesion) rates on a pure quartz surface. The outer surface potential failed to predict the low attachment efficiencies of the two bacterial strains. The lack of success in the application of the theory for soft particles to bacterial cells is attributed to chemical and physical heterogeneities of the polyelectrolyte layer at the cell surface.     

Colloid Vibration Potential in a Concentrated Suspension of Spherical Colloidal Particles

A relation between the dynamic electrophoretic mobility of spherical colloidal particles in a concentrated suspension and the colloid vibration potential (CVP) generated in the suspension by a sound wave is obtained from the analogy with the corresponding Onsager relation between electrophoretic mobility and sedimentation potential in concentrated suspensions previously derived on the basis of Kuwabara's cell model. The obtained expression for CVP is applicable to the case where the particle zeta potential is low, the particle relative permittivity is very small, and the overlapping of the electrical double layers of adjacent particles is negligible. It is found that CVP shows much stronger dependence on the particle volume fraction φ than predicted from the φ dependence of the dynamic electrophoretic mobility. It is also suggested that the same relation holds between the electrokinetic sonic amplitude of a concentrated suspension of spherical colloidal particles and the dynamic electrophoretic mobility. Copyright 1999 Academic Press.     

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.     

Influence of membrane layer properties on the electrophoretic behavior of a soft particle

The influence of the physical properties of the membrane layer of a soft particle, which comprises a rigid core and a porous membrane layer, on its electrophoretic behavior, is investigated. Because that influence was almost always neglected in the previous studies, the corresponding results can be unrealistic. The applicability of the model proposed is verified by the available theoretical and experimental results. The electrophoretic mobility of the particle under various conditions is simulated through varying the dielectric constant, the thickness, and the drag coefficient of the membrane layer, and the bulk ionic concentration. We show that under typical conditions, the deviation in the electrophoretic mobility arising from assuming that the dielectric constant of the membrane layer is the same as that of the bulk liquid phase can be in the order of 50%. In addition, the thicker the membrane layer and/or the higher the bulk ionic concentration, the larger the deviation. If the surface of the core of the particle is charged, as in the case of inorganic particles covered by an artificial membrane layer, the deviation at constant core surface potential is larger than that under other types of charged conditions. However, if the surface of the core is uncharged, as in the case of biocolloids, then that deviation becomes negligible. These findings are of fundamental significance to theoreticians in their analysis on the electrokinetic behaviors of soft particles, and to experimentalists in the interpretation of their data.     

Separation of Nucleic Acid Constituents by Column Liquid Chromatography

As a general rule the electrophoretic mobility of molecules and particles is solely governed by the potential at their surface of shear (ζ-potential) and does not depend on their size or shape. There are hawever two sets of exceptional conditions under which the size or shape of molecules and particles may influence their electrophoretic mobility. These are:

1) Conditions under which the ratio between the dimensions of the molecules or particles and the thickness of their diffuse ionic double layer is such that the distortion of the electric field by the particles is neither at its minimum nor at its maximum.

2) Conditions under which the molecules or particles are migrating under the influence of an electric field inside a porous medium, the size of the pores of which is such that they impede the larger molecules or particles more than the smaller ones.     

Dynamic Electrophoretic Mobility of a Soft Particle

A theory of the dynamic electrophoretic mobility of a spherical soft particle (that is, a polyelectrolyte-coated spherical particle) in an oscillating electric field is presented. In the absence of the polyelectrolyte layer a spherical soft particle becomes a spherical hard particle, while in the absence of the particle core it tends to a spherical polyelectrolyte. The present theory thus covers two extreme cases, that is, dynamic electrophoresis of hard particles and that of spherical polyelectrolytes. Simple analytic mobility expressions are derived. It is shown how the dynamic electrophoretic mobility of a soft particle depends on the volume charge density distributed in the polyelectrolyte layer, on the frictional coefficient characterizing the frictional forces exerted by the polymer segments on the liquid flow in the polyelectrolyte layer, on the particle size, and on the frequency of the applied oscillating electric field. Copyright 2001 Academic Press.     

Electrophoretic mobility of a colloidal particle with constant surface charge density

When the electrophoretic mobility of a particle in an electrolyte solution is measured, the obtained electrophoretic mobility values are usually converted to the particle zeta potential with the help of a proper relationship between the electrophoretic mobility and the zeta potential. For a particle with constant surface charge density, however, the surface charge density should be a more characteristic quantity than the zeta potential because for such particles the zeta potential is not a constant quantity but depends on the electrolyte concentration. In this article, a systematic method that does not require numerical computer calculation is proposed to determine the surface charge density of a spherical colloidal particle on the basis of the particle electrophoretic mobility data. This method is based on two analytical equations, that is, the relationship between the electrophoretic mobility and zeta potential of the particle and the relationship between the zeta potential and surface charge density of the particle. The measured mobility values are analyzed with these two equations. As an example, the present method is applied to electrophoretic mobility data on gold nanoparticles (Agnihotri, S. M.; Ohshima, H.; Terada, H.; Tomoda, K.; Makino, K. Langmuir 2009, 25, 4804).     

Electrophoretic motion of a slightly deformed sphere with a nonuniform zeta potential distribution

Electrophoretic motion is analyzed for a rigid, slightly deformed sphere with a nonuniform zeta potential distribution. Hydrodynamics and electrostatics solutions for the deformed sphere with an arbitrary double-layer thickness are determined by using the domain perturbation method. The surface shape and the zeta potential distribution for the deformed sphere are expressed by using the multipole expansion representation. In terms of monopole, dipole, and quadrupole moments of the surface shape and the zeta potential distribution, explicit expressions are obtained for the translational and rotational electrophoretic mobility tensors. The ensemble average for the mobility of the deformed sphere with a uniform orientation distribution is also derived. The utility of the general mobility expression is demonstrated by studying the electrophoretic motion of axisymmetric and ellipsoidal particles. The translational and rotational mobilities of axisymmetric particles are both affected by the monopole, dipole, and quadrupole moments of the zeta potential. For ellipsoidal particles, however, the dipole moment of the zeta potential does not affect the translational mobility, while the rotational mobility depends only on the dipole moment. The mobility of the deformed sphere with either a thick or a thin double layer is also derived.     

Approximate analytic expressions for the electrophoretic mobility of spherical soft particles

Approximate analytic expressions are derived for the electrophoretic mobility of a weakly charged spherical soft particle consisting of the particle core covered with a surface layer of polymers in an electrolyte solution. The particle core and the surface polymer layer may be charged or uncharged. The obtained electrophoretic mobility expressions, which involve neither numerical integration nor exponential integrals, are found to be in excellent agreement with the exact numerical results. It is also found that the obtained mobility expressions reproduce all the previously derived limiting expressions and approximate analytic expressions for the electrophoretic mobility of a weakly charged spherical soft particle.