Determination of Polymer Effective Charge by Indirect UV Detection in Capillary Electrophoresis: Toward the Characterization of Macromolecular Architectures

Determination of physicochemical parameters of (bio)molecules and (bio)particles by capillary electromigration methods

The review provides an overview of recent developments and applications of capillary electromigration (CE) methods for the determination of important physicochemical parameters of various (bio)molecules and (bio)particles. These parameters include actual and limiting (absolute) ionic mobilities, effective electrophoretic mobilities, effective charges, isoelectric points, electrokinetic potentials, hydrodynamic radii, diffusion coefficients, relative molecular masses, acidity (ionization) constants, binding constants and stoichiometry of (bio)molecular complexes, changes of Gibbs free energy, enthalpy and entropy and rate constants of chemical reactions and interactions, retention factors and partition and distribution coefficients. For the determination of these parameters, the following CE methods are employed: zone electrophoresis in a free solution or in sieving media, isotachophoresis, isoelectric focusing, affinity electrophoresis, electrokinetic chromatography, and electrochromatography. In the individual sections, the procedures for the determination of the above parameters by the particular CE methods are described.

Using capillary electrophoresis to characterize the hydrodynamic and electrostatic properties of DNA in solutions containing various monovalent cations

This review describes the results obtained by using free-solution capillary electrophoresis to probe the electrostatic and hydrodynamic properties of DNA in solutions containing various monovalent cations. In brief, we found that the mobilities of double-stranded DNAs (dsDNAs) increase with increasing molecular weight before leveling off and becoming constant at molecular weights ≥400 bp. The mobilities of single-stranded DNAs (ssDNAs) go through a maximum at ∼10-20 nucleotides before decreasing and becoming constant for oligomers larger than ∼30-50 bases. The mobilities of both ss- and dsDNAs increase linearly with the logarithm of increasing charge per unit length and decrease linearly with the logarithm of increasing ionic strength. Surprisingly, ss- and dsDNA mobilities level off and become nearly constant at ionic strengths ≥0.6 M. The thermal stabilities of dsDNAs decrease linearly with increasing solution viscosity. The diffusion coefficients of dsDNA are modulated by the diffusion coefficients of their counterions because of electrostatic DNA-cation coupling interactions. Finally, the anomalously slow mobilities observed for A-tract-containing DNAs can be attributed both to differences in shape and to the preferential localization of small cations in the A-tract minor groove. Since many of these results are mirrored in other polyion-counterion systems, free-solution electrophoresis can be viewed as a reporter of the electrostatics and hydrodynamics of highly charged polyions. New results describing the mobilities of dsDNA analogues of a microRNA-messenger RNA complex are also presented.

Counterion Exchange in Peptide-Complexed Core-Shell Microgels

The complexation of polyvalent macroions with oppositely charged polyelectrolyte microgels can lead to core-shell structures. The shell is believed to be highly deswollen with a high concentration of counter-macroions. The core is believed to be relatively free of macroions but under a uniform compressive stress due to the deswollen shell. We use cryo-scanning electron microscopy (SEM) with X-ray microanalysis to confirm this understanding. We study poly(acrylic acid) (PAA) microgels which form a core-shell structure when complexed with a small cationic antimicrobial peptide (L5). We follow the spatial distribution of polymer, water, Na counterions, and peptide based on the characteristic X-ray intensities of C, O, Na, and N, respectively. Frozen-hydrated microgel suspensions include buffers of known composition from which calibration curves can be generated and used to quantify both the microgel water and sodium concentrations, the latter with a minimum quantifiable concentration less than 0.048 M. We find that as-synthesized PAA microgels are enriched in Na relative to the surrounding buffer as anticipated from established ideas of counterion shielding of electrostatic charge. The shell in L5-complexed microgels is depleted in Na and enriched in peptide and contains relatively little water. Our measurements furthermore show that shell/core interface is diffuse over a length scale of a few micrometers. Within the limits of detection, the core Na concentration is the same as that in as-synthesized microgels, and the core is free of peptide. The core has a slightly lower water concentration than as-synthesized controls, consistent with the hypothesis that the core is under compression from the shell.

Effect of Dendrigraft Generation on the Interaction between Anionic Polyelectrolytes and Dendrigraft Poly(l-Lysine)

In this present work, three generations of dendrigraft poly(l-Lysine) (DGL) were studied regarding their ability to interact with linear poly (acrylamide-co-2-acrylamido-2-methyl-1-propanesulfonate) (PAMAMPS) of different chemical charge densities (30% and 100%). Frontal analysis continuous capillary electrophoresis (FACCE) was successfully applied to determine binding constants and binding stoichiometries. The effect of DGL generation on the interaction was evaluated for the first three generations (G2, G3, and G4) at different ionic strengths, and the effect of ligand topology (linear PLL vs. dendrigraft DGL) on binding parameters was evaluated. An increase of the biding site constants accompanied with a decrease of the DGL-PAMAMPS (n:1) stoichiometry was observed for increasing DGL generation. The logarithm of the global binding constants decreased linearly with the logarithm of the ionic strength. This double logarithmic representation allowed determining the extent of counter-ions released from the association of DGL molecules onto one PAMAMPS chain that was compared to the total entropic reservoir constituted by the total number of condensed counter-ions before the association.

Electrophoretic Mobilities of the Charge Variants of DNA and Other Polyelectrolytes: Similarities, Differences, and Comparison with Theory

Free solution electrophoretic mobilities of polyelectrolytes with different charge densities have been analyzed using data taken from the literature. The polyions include single- and double-stranded DNA oligomers, small aromatic molecules, peptides, proteins, and synthetic copolymers. Mobility variations due to differences in the background electrolytes were minimized by calculating mobility ratios, dividing the mobility of each charge variant in each data set by the mobility of the most highly charged polyion in that data set. In all cases, the mobility ratios increase linearly with the logarithm of the fractional charge, not the first power of the charge as usually assumed. In addition, the mobility ratios observed for all polyelectrolytes, except for the synthetic copolymers, exhibit a common dependence on the logarithm of fractional charge. The unique results observed for the synthetic copolymers may be due to the flexibility of their hydrocarbon backbones, in contrast to the relatively rigid hydrophilic backbones of the other polyelectrolytes. The mobilities observed for the DNA charge variants are well predicted by the Manning electrophoresis equation, whereas the mobilities predicted by zeta potential theories are higher. However, mobility ratios calculated from both theories agree with the observed results.

Analysis and characterization of aluminum chlorohydrate oligocations by capillary electrophoresis

Aluminum chlorohydrates (ACH) are the active ingredients used in most antiperspirant products. ACH is a water soluble aluminum complex which contains several oligomeric polycations of aluminum with degrees of polymerization up to Al₁₃ or Al₃₀. The characterization and quantification of ACH oligo-cations remain a challenging issue of primary interest for developing structure/antiperspirant activity correlations, and for controlling the ACH ingredients. In this work, highly repeatable capillary electrophoresis (CE) separation of A_l3⁺, Al₁₃ and Al₃₀ oligomers contained in ACH samples was obtained at pH 4.8, owing to a careful choice of the background electrolyte counter-ion and chromophore, capillary I.D. and capillary coating. This is the first reported separation of Al₁₃ and Al₃₀ oligomers in conditions that are compatible with the aluminum speciation in ACH solution or in conditions of antiperspirant application/formulation. Al₁₃ and Al₃₀ effective charge numbers were also determined from the sensitivity of detection in indirect UV detection mode. The relative mass proportion of Al₁₃ compared to Al₁₃+Al₃₀ could be determined in different aluminum chlorohydrate samples. Due to its simplicity, repeatability/reproducibility, minimal sample preparation and mild analytical conditions, CE appears to be a promising analytical separation technique for the characterization of ACH materials and for the study of structure/antiperspirant activity correlations.

The Effect of Molar Mass and Charge Density on the Formation of Complexes between Oppositely Charged Polyelectrolytes

The interactions between model polyanions and polycations have been studied using frontal continuous capillary electrophoresis (FACCE) which allows the determination of binding stoichiometry and binding constant of the formed polyelectrolyte complex (PEC). In this work, the effect of the poly(l-lysine) (PLL) molar mass on the interaction with statistical copolymers of acrylamide and 2-acrylamido-2-methyl-1-propanesulfonate (PAMAMPS) has been systematically investigated for different PAMAMPS chemical charge densities (15% and 100%) and different ionic strengths. The study of the ionic strength dependence of the binding constant allowed the determination of the total number of released counter-ions during the formation of the PEC, which can be compared to the total number of counter-ions initially condensed on the individual polyelectrolyte partners before the association. Interestingly, this fraction of released counter-ions, which was strongly dependent on the PLL molar mass, was almost independent of the PAMAMPS charge density. These findings are useful to predict the binding constant according to the molar mass and charge density of the polyelectrolyte partners.

Modelling and predicting the interactions between oppositely and variously charged polyelectrolytes by frontal analysis continuous capillary electrophoresis

In this work, a systematic study of the interactions between poly(l-lysine) and variously charged statistical copolymers of acrylamide and 2-acrylamido-2-methyl-1-propanesulfonate (PAMAMPS) has been carried out by frontal analysis continuous capillary electrophoresis (FACCE). FACCE was successfully implemented to obtain the interaction parameters (binding constant and stoichiometry) at different ionic strengths and for different PAMAMPS charge densities varying between 15% and 100%. The range of investigated ionic strengths was carefully adjusted according to the PAMAMPS charge density to obtain measurable binding constants by FACCE (i.e. formation binding constant typically comprised between 10⁴ and 10⁶ M^-1). The number of released counter-ions during the polyelectrolyte complex formation was systematically quantified via the ionic strength dependence of the binding constant and was compared to the total condensed counter-ion reservoir according to Manning theory on counter-ion condensation. A descriptive and predictive model relating the physico-chemical properties of the two partners, the binding constant and the ionic strength is proposed in the framework of multiple independent interaction sites of equal energy.

Size and charge characterization of polymeric drug delivery systems by Taylor dispersion analysis and capillary electrophoresis

In this work, Taylor dispersion analysis and capillary electrophoresis were used to characterize the size and charge of polymeric drug delivery nanogels based on polyglutamate chains grafted with hydrophobic groups of vitamin E. The hydrophobic vitamin E groups self-associate in water to form small hydrophobic nanodomains that can incorporate small drugs or therapeutic proteins. Taylor dispersion analysis is well suited to determine the weight average hydrodynamic radius of nanomaterials and to get information on the size polydispersity of polymeric samples. The effective charge was determined either from electrophoretic mobility and hydrodynamic radius using electrophoretic modeling (three different approaches were compared), or by indirect UV detection in capillary electrophoresis. The influence of vitamin E hydrophobicity on the polymer effective charge has been studied. The presence of vitamin E leads to a drastic decrease in polymer effective charge in comparison to non-modified polyglutamate. Finally, the electrophoretic behavior of polyglutamate backbone grafted with hydrophobic vitamin E (pGVE) nanogels according to the ionic strength was investigated using the recently proposed slope plot approach. It was deduced that the pGVE nanogels behave electrophoretically as polyelectrolytes which is in good agreement with the high water content of the nanogels.

Determination of effective charge of small ions, polyelectrolytes and nanoparticles by capillary electrophoresis

In this paper, a systematic and comparative study related to the effective charge determination of three kinds of solutes (small ions, polyelectrolytes and nanoparticles) was performed. Four approaches were compared regarding their conditions of validity and their advantages/disadvantages. Three of them allow the effective charge determination from the electrophoretic mobility and the hydrodynamic radius of the solutes using electrophoretic mobility modelings based on Nernst-Einstein (NE), O'Brien-White-Ohshima (OWO) and Yoon and Kim (YK) equations. Electrophoretic mobility and hydrodynamic radius were determined by capillary electrophoresis and Taylor dispersion analysis, respectively, using the same instrumentation in similar conditions, on a large set of samples. A fourth experimental approach based on the sensitivity of detection in indirect UV detection mode (IUV) was compared to the previously mentioned methods. OWO and YK modelings are well adapted for the effective charge determination of small ions and nanoparticles, while IUV is the only method adapted for polyelectrolytes.

Characterization of Gellan Gum by Capillary Electrophoresis

Gellan gums were characterised for the first time using free-solution capillary electrophoresis (CE) or CE under critical conditions (CE-CC). CE-CC is a fast method that separates the polysaccharide. Gellan gums are shown to be heterogeneous in terms of their electrophoretic mobility at 55°C revealing: oligomer peak(s), broad peaks of polymers with a random coil conformation with different degrees of acylation (composition), aggregates, and polymers with double-helix conformation. CE-CC is complementary with the rheological analysis also performed in this work. Sonication of gellan gums is shown to decrease the viscosity of gellan gum mainly by breaking up aggregates. The effect of sonication is stronger on the high-acyl gellan gum since the latter has a far higher tendency to aggregate.

Counterion condensation and shape within Poisson-Boltzmann theory

An analytical approximation to the nonlinear Poisson-Boltzmann (PB) equation is applied to charged macromolecules that possess one-dimensional symmetry and can be modeled by a plane, infinite cylinder, or sphere. A functional substitution allows the nonlinear PB equation subject to linear boundary conditions to be transformed into an approximate linear (Debye-Hückel-type) equation subject to nonlinear boundary conditions. A simple analytical result for the surface potential of such polyelectrolytes follows, leading to expressions for the amount of condensed (or renormalized) charge and the electrostatic Helmholtz energy for polyelectrolytes. Analytical high-charge/low-salt and low-charge/high-salt limits are shown to be similar to results obtained by others based on PB or counterion condensation theory. Several important general observations concerning polyelectrolytes treated within the context of PB theory can be made including: (1) all charged surfaces display some counterion condensation for finite electrolyte concentration, (2) the effect of surface geometry is described primarily by the sum of the Debye constant and the mean curvature of the surface, (3) two surfaces with the same surface charge density and mean curvature condense approximately identical fractions of counterions, (4) the amount of condensation is not determined by a predefined "condensation distance" although such a distance can be determined uniquely from it, and (5) substantial condensation occurs if the Debye constant of the electrolyte is much less than the mean curvature of a highly charged polyelectrolyte.