Use of CE for the determination of binding constants

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.

Determination of the binding constants and ionic mobilities of diquat complexes with randomly sulfated cyclodextrins by affinity capillary electrophoresis

The enantiomers of diquats (DQs), a new class of functional organic molecules, were recently separated by capillary electrophoresis (CE) with high resolution up to 11.4 within 5-7 min using randomly sulfated α-, β-, and γ-cyclodextrins (CDs) as chiral selectors. These results indicated strong interactions between dicationic diquats and multiply negatively charged sulfated CDs (S-CDs). However, the binding strength of these interactions was not quantified. For that reason, in this study, affinity CE was applied for the determination of the binding constants and ionic mobilities of the complexes of DQ P- and M-enantiomers with CD chiral selectors in an aqueous medium. The non-covalent interactions of 10 pairs of DQ enantiomers with the above CDs were investigated in a background electrolyte (BGE) composed of 22 mM NaOH, 35 mM H3PO4, pH 2.5, and 0.0-1.0 mM concentrations of CDs. The average apparent binding constant and the average actual ionic mobility of the DQ-CD complexes were determined by nonlinear regression analysis of the dependence of the effective mobility of DQ enantiomers on the concentration of CDs in the BGE. The complexes were found to be relatively strong with the averaged apparent binding constants in the range 13 600-547 400 L/mol.

Moment Analysis Method for Measurement of Reaction Equilibrium and Rate Constants by Using High-Performance Liquid Chromatography

The moment analysis method was developed for the determination of association equilibrium constant (KA) and association (ka) and dissociation (kd) rate constants of intermolecular interactions between solute and ligand molecules. They are accurately determined by using moment equations from elution peak profiles because they are measured by using high-performance liquid chromatography (HPLC) under preferable conditions that neither immobilization nor chemical modification (i.e., fluorescence labeling) of solute and ligand molecules is required. To demonstrate the effectiveness of the method, it was applied to the inclusion complex formation system between dibenzo-18-crown-6 (DB18C6) and alkaline earth metal cations, i.e., Mg2+, Ca2+, and Sr2+, as a concrete example. Because the diameter of the three metal cations is smaller than that of the inner cavity of DB18C6, the values of KA, ka, and kd were analytically determined by assuming the stoichiometry of 1:1 between DB18C6 and the metal cation. They reflected the influence of the difference in the size between the inner cavity of DB18C6 and the metal cations on the inclusion complex formation. It seems that the moment analysis method based on HPLC separation is effective for the multifaceted analysis of chemical reactions because some characteristics of the method are different from those of other conventional methods. It must contribute to the dissemination of an opportunity for the study of chemical reactions to many researchers because of the versatility of HPLC.

Affinity Capillary Electrophoresis as a Tool To Characterize Molecularly Imprinted Nanogels in Solution

In this work, an innovative and accurate affinity capillary electrophoresis (ACE) method was set up to monitor the complexation of aqueous MIP nanogels (NGs) with model cancer-related antigens. Using α2,6'- and α2,3'-sialyllactose as oversimplified cancer biomarker-mimicking templates, NGs were synthesized and characterized in terms of size, polydispersity, and overall charge. A stability study was also carried out in order to select the best storage conditions and to ensure product quality. After optimization of capillary electrophoresis conditions, injection of MIP NGs resulted in a single, sharp, and efficient peak. The mobility shift approach was applied to quantitatively estimate binding affinity, in this case resulting in an association constant of K ≈ 106 M-1. The optimized polymers further displayed a pronounced discrimination between the two sialylated sugars. The newly developed ACE protocol has the potential to become a very effective method for nonconstrained affinity screening of NG in solution, especially during the NG development phase and/or for a final accurate quantitation of the observed binding.

The affinity of histamine to serum albumin: Capillary electrophoresis-frontal analysis and in-silico molecular docking approaches

Histamine is a biogenic amine found in various body tissues and responsible for many critical vital activities. It is also responsible for allergic reactions in the body. Ingestion of foods containing high amounts of histamine can cause fatal allergic reactions. Albumin in plasma controls drugs and free concentrations of bioactive constituents taken to the body with food. Hence, this study aimed to characterise the interactions of histamine with bovine serum albumin. Capillary electrophoresis in the frontal analysis mode was employed in this study as a practical approach for assessing histamine-bovine serum albumin affinity. The plateau-shaped free histamine peak was well separated from the bovine serum albumin (BSA)-histamine complex peak. The free histamine concentration was obtained by following the height of the free histamine peak. Whereas the bound histamine concentrations were obtained by calculating the difference between the height of total and free histamine peaks. Histamine bound to BSA at one independent site with a Kb value of 2.50 × 103 L/mol. Moreover, an in-silico molecular docking method was performed, and it was revealed that the binding site of histamine was located closer to Lysine-131 in subdomain IIA of bovine serum albumin.

Studying protein structure and function by native separation–mass spectrometry

Alterations in protein structure may have profound effects on biological function. Analytical techniques that permit characterization of proteins while maintaining their conformational and functional state are crucial for studying changes in the higher order structure of proteins and for establishing structure-function relationships. Coupling of native protein separations with mass spectrometry is emerging rapidly as a powerful approach to study these aspects in a reliable, fast and straightforward way. This Review presents the available native separation modes for proteins, covers practical considerations on the hyphenation of these separations with mass spectrometry and highlights the involvement of affinity-based separations to simultaneously obtain structural and functional information of proteins. The impact of these approaches is emphasized by selected applications addressing biomedical and biopharmaceutical research questions.

Boundary values of binding constants determined by affinity capillary electrophoresis

This study shows that the upper limit of binding (stability) constants determined by mobility shift affinity capillary electrophoresis can be increased from 10⁴ to 10⁶ -10⁹ L/mol if the lowest possible analyte concentration in samples is used (for example, the concentration that gives electrophoretic peaks with a signal-to-noise ratio of 10) and the effective electrophoretic mobility of the analyte is calculated via the parameter a₁ of the Haarhoff-Van der Linde function. The equation to calculate the boundary values of binding constants for 1:1 complexes was derived for the case when the constants cannot be calculated in the usual way. These values are obtained from the inequality: the difference between the ionic mobility of the analyte-ligand complex and the effective electrophoretic mobility of the analyte determined at the lowest ligand concentration in the background electrolyte at which the analyte appears as an undistorted peak in electropherograms is less than or equal to the absolute error in mobility measurements. The application of the equation was illustrated by the example of electrophoretic data for a complex between betulin 3,28-diphthalate and (2-hydroxypropyl)-γ-cyclodextrin. An algorithm to determine the binding constants for strong complexation by mobility shift affinity capillary electrophoresis was suggested.

Moment Theory of Chromatography for the Analysis of Reaction Kinetics of Intermolecular Interactions

Moment theory was applied to the kinetic study of intermolecular interactions. The association equilibrium constant (K_A) and association (k_a) and dissociation (k_d) rate constants of chemical reactions were analytically determined on the basis of the moment theory from elution peak profiles measured by high-performance liquid chromatography (HPLC). The HPLC data were measured under the conditions that neither immobilization nor fluorescence labeling of solute and ligand molecules is required. These are the advantages of the moment analysis method for determining accurate values of K_A, k_a, and k_d. Moment equations were developed on the basis of the Einstein equation for diffusion, the random walk model, and the general rate model of chromatography. The moment analysis method was applied to the inclusion complex formation system between dibenzo-18-crown-6 or dibenzo-15-crown-5 and alkali metal cations. It was demonstrated that the values of K_A, k_a, and k_d can be determined on the assumption that the stoichiometry between crown ethers and cations is 1:1 or 2:1. The influence of the difference in the size between the inner cavity of crown ethers and cations on the association and dissociation of the inclusion complex was considered. The moment analysis method using HPLC is effective for analyzing intermolecular interactions from various perspectives because it is based on the separation technique and has different characteristics from other methods such as spectroscopy. The results of this study contribute to the dissemination of an opportunity for studying intermolecular interactions from equilibrium and kinetic points of view to many researchers because HPLC is widespread.

Assignment of complex species by affinity capillary electrophoresis: The case of Th(IV)-desferrioxamine B

The electrophoretic mobility change of desferrioxamine B (DFO) was monitored by UV absorption spectrophotometry upon increasing the thorium(IV) concentration in the background electrolyte at two acidities ([HClO₄ ]_Tot = 0.0316 and 0.0100 M). These data enabled to assess the speciation model and to determine the equilibrium constant of [Th(DFO)H₂ ]³⁺ at fixed ionic strength (I = 0.1 M (H,Na)ClO₄ ). Affinity capillary electrophoresis (ACE) turned out to be most helpful in identifying the complexed species by ascertaining its charge and protonation state. The assignment of the correct stoichiometry relied on the reliable estimation of the electrophoretic mobility by assuming similar hydrodynamic radii for (DFO)H₄ ⁺ and the chelate. The value of the apparent equilibrium constant (log β₁₁₂ = 38.7 ± 0.4) obtained by ACE compares favorably well with those reported in the literature for thorium and a range of other metal ions, according to a linear free-energy relationship. This method is useful for studying metal-ligand binding equilibria and provides valuable information for further modelling the behavior of tetravalent actinides under environmental conditions. Structural information about the prevalent solution species in acidic conditions was gained by DFT calculations, confirming the bishydroxamato coordination mode of Th⁴⁺ by the diprotonated ligand.

Study of interactions between carboxylated core shell magnetic nanoparticles and polymyxin B by capillary electrophoresis with inductively coupled plasma mass spectrometry

In this work, interactions of carboxylated core shell magnetic nanoparticles with polymyxin B sulfate were studied by connecting capillary electrophoresis with inductively coupled plasma mass spectrometry. The interaction was probed by affinity mode of capillary electrophoresis with 25 mM phosphate buffer at physiological pH. ⁵⁴Fe, ⁵⁶Fe, ⁵⁷Fe, ³⁴S, and ¹²C isotopes were used to monitor the migration of an electroosmotic flow marker and the interaction of the nanoparticles with polymyxin B. The analysis of interaction data showed two distinct interaction regions, one with low polymyxin B concentration, the second with high polymyxin B concentration. These regions differed in the strength of the interaction, 1.49 × 10⁷ M^-1 and 1.60 × 10⁴ M^-1, and in the stoichiometry of 0.7 and 3.5, respectively. These differences can be explained by the decrease of electrostatic repulsion between nanoparticles caused by polymyxin B. This is also in agreement with the nanoparticles peak shapes: sharp for low polymyxin B concentrations and broad for high polymyxin B concentrations.

N-acetylcysteine dual and antagonistic effect on cadmium cytotoxicity in human leukemia cells

Although cadmium (Cd²⁺) is unable to form reactive oxygen species (ROS) directly, many of its adverse effects are connected to increased ROS generation resulting in cell death. In support of this supposition, a large number of studies have shown protective effects of antioxidants such as N-acetylcysteine (NAC) against cadmium induced cytotoxicity. Here, we describe the cytotoxic effects of Cd²⁺ on human leukemia U937 and K562 cells that were not mediated by oxidative stress. Surprisingly, we observed that addition of low concentrations of NAC can drastically potentiate cadmium cytotoxicity solely via ROS production. However, all adverse effects of the metal were prevented by NAC at high concentrations. Detailed analysis indicated that the protective effect of NAC was mediated by its ability to form stable complex with cadmium [Cd(NAC)₂]. In conclusion, NAC exhibits dual and antagonistic effects on Cd²⁺ cytotoxicity in human leukemia cells.

Clinical and pharmaceutical applications of affinity ligands in capillary electrophoresis: A review

Affinity capillary electrophoresis (ACE) is a separation technique that combines a biologically-related binding agent with the separating power and efficiency of capillary electrophoresis. This review will examine several classes of binding agents that have been used in ACE and applications that have been described for the resulting methods in clinical or pharmaceutical analysis. Binding agents that will be considered are antibodies, aptamers, lectins, serum proteins, carbohydrates, and enzymes. This review will also describe the various formats in which each type of binding agent has been used in CE, including both homogeneous and heterogeneous methods. Specific areas of applications that will be considered are CE-based immunoassays, glycoprotein/glycan separations, chiral separations, and biointeraction studies. The general principles and formats of ACE for each of these applications will be examined, along with the potential advantages or limitations of these methods.

Determination of kinetic parameters of redox reactions using CE-ICP-MS: A case study for the reduction of Np(V) by hydroxylamine hydrochloride

The rate constants k of the reduction of 5 × 10^-5  M Np(V) to Np(IV) by hydroxylamine hydrochloride (HAHCl) in 1 M HCl have been determined by CE-ICP-MS in the temperature range of ϑ = 30-70°C and with varying concentrations of HAHCl from 1 to 7.2 M. The reaction was found to have (pseudo)first order kinetics with respect to HAHCl. The experimental results for k ranged from 0.0029(1) min^-1 (ϑ = 40°C, c(HAHCl) = 3 M) to 0.039(7) min^-1 (ϑ = 60°C, c(HAHCl) = 7.2 M). The activation energy of the reaction was determined as E_A  = (72 ± 10) kJ/mol. These results and a comparison with literature data show that the coupling of CE to ICP-MS provides a powerful analytical tool for the investigation of the kinetic aspects of redox reactions of actinides at low concentrations. On the basis of this proof-of-principle study, the method presented here can be extended to the investigation of the kinetic parameters of other redox systems containing different actinides (or transition metals) and oxidants/reductants.

Determination of thermodynamic binding constants by affinity capillary electrophoresis

A strategy to study thermodynamic binding constants by affinity capillary electrophoresis (ACE) is presented. In order to simplify mathematical treatment, analogy with acid-base dissociation equilibrium is proposed: instead of ligand concentration [X], negative logarithm of ligand concentration (or activity), pX = -log[X], is used. On this base, and taking into account ionic activities, a general procedure for obtaining thermodynamic binding constants is proposed. In addition, the method provides electrophoretic mobilities of the free analyte and analyte-ligand complex, even when binding constants are low and thus, the complexed analyte fraction is also low. This is useful as a base to rationally analyze a diversity of situations, i.e., different mathematical dependencies are obtained when analytes and ligands with different charges are combined. Practical considerations are given for carrying out a full experimental design. Enantiomeric ACE separation based on the use of chiral selectors is addressed. 2-hydroxypropyl-β-cyclodextrin was chosen as a model ligand, and both enantiomeric forms of four pharmaceutical drugs (propranolol, pindolol, oxprenolol and homatropine methylbromide) were considered as model analytes. Practical aspects are detailed and thermodynamic binding constants as well as free and complexed analytes mobilities are determined.

Moment analysis for reaction kinetics of intermolecular interactions

Moment equations were developed on the basis of the principle of relativity for analyzing elution peak profiles measured by ACE to analytically determine the association (k_a ) and dissociation (k_d ) rate constants of intermolecular interactions. Basic equations representing the mass balance, mass transfer rate, and reaction kinetics in ACE system in a Galilean coordinate system S were transformed to those in another coordinate system S', which imaginarily moved with respect to S. Moment equations for ACE peaks in S' in the time domain were derived from the analytical solution of the modified basic equations in the Laplace domain. Moment equations for ACE peaks in S were derived from those in S' by the inverse Galilean transformation. The moment equations were used for analyzing some ACE data previously published to determine k_a and k_d values. It was demonstrated that the moment equations were effective for extracting the information about affinity kinetics of intermolecular interactions from the elution peak profiles measured by ACE. The moment equations were also used to discuss the influence of mass transfer and reaction kinetics on ACE peak profiles. Some results of the numerical calculations are also indicated in Supporting Information.

Frontal analysis capillary electrophoresis: recent advances and future perspectives

The developments on frontal analysis capillary electrophoresis (FACE) from 2012 to 2017 to study interactions of simple and complex systems are reviewed. Most research papers focused on therapeutic drug-related studies; however, other studies include chemical sensing, drug delivery, inhibitor screening and capillary coating. New ligand–substrate systems such as template-molecularly imprinted polymer systems were reported. Comparison of FACE with other analytical techniques used to investigate binding interaction, and the determination of binding parameters using different isotherm models are also covered. In 2017, eight research papers were reported including new detection by ESI–MS. Future research direction of FACE may include high sensitivity detection and throughput screening of drugs, natural products and biomarkers for clinical diagnosis.

Complexation of An(vi) with succinic acid in aqueous acid solutions: uranyl vs. plutonyl

Due to stronger electrostatic interaction in a uranyl–succinate system, complex species of U(vi) with succinate are more stable than the ones of Pu(vi).

Effects of preorganization in the chelation of UO22+by hydroxamate ligands: cyclic PIPO−vs.linear NMA−

Thanks to preorganization, 1,2-PIPOH, the six-membered ring cyclic hydroxamic acid, binds uranyl six times more strongly than its linear, methyl-substituted homolog (NMAH).

Moment Analysis Theory for Size Exclusion Capillary Electrochromatography with Chemical Reaction of Intermolecular Interaction

New moment equations were developed for size exclusion capillary electrochromatography (SECEC), in which intermolecular chemical reactions simultaneously took place. They explain how the first absolute and second central moments of elution peaks are correlated with some fundamental equilibrium and kinetic parameters of mass transfer and chemical reaction in SECEC column. In order to demonstrate the effectiveness of the moment equations, they were used to predict chromatographic behavior under hypothetical SECEC conditions. It was quantitatively studied how the association and dissociation rate constants of intermolecular interaction affected the position and spreading of elution peaks. It was indicated that both the intermolecular reaction kinetics and axial dispersion of solute molecules in a capillary column had a predominant contribution to the band broadening.

Seven Approaches to Elimination of the Inherent Systematic Errors in Determination of Electrophoretic Mobility by Capillary Electrophoresis

Electrophoretic mobility is a basic parameter that describes the electromigration of an ionized particle, which is used in many fields of analytical and physicochemical science. Its determination by capillary electrophoresis (CE), using a routine method, is intrinsically affected by the generation of Joule heating, entailing a drop in viscosity and possible alteration of the degree of ionization, and also by other commonly overlooked effects: axial electric field distortion and voltage ramping. The objective of this work was to provide the first theoretical overview and experimental comparison of all accessible methods that could be used to prevent these sources of inaccuracy. We have discussed seven independent approaches: (i) extrapolation of mobility to the zero power, (ii) initial buffer resistance-based correction, (iii) rational cooling adjustment, (iv) elimination of the nonthermostated capillary part, (v) inter/extrapolation to the nominal temperature, (vi) internal standard-based correction, and (vii) simple recalculation based on the temperature rise. Two methodologies (v and vi) have been proposed for the first time. Furthermore, we have shown how some approaches can be further developed, obtaining several novel and more sophisticated methods, which are also included in the comparison. Our investigation will help researchers to choose the optimal approach. We have also demonstrated for the first time how to measure the independent impact of four different effects. The outcomes reveal the compensatory character of some phenomena and explain the highly diverse and unpredictable magnitude of the total errors. The use of a correction method seems crucial for ensuring the high reliability of CE-based analyses.

Affinity capillary electrophoresis and quantum mechanical calculations applied to investigation of [Gly6 ]-antamanide binding with sodium and potassium ions

ACE in a free solution and quantum mechanical density functional theory have been applied to the investigation of interactions of glycine-6-antamanide ([Gly⁶ ]AA), a synthetic derivative of cyclic decapeptide antamanide isolated from the highly poisonous mushroom Amanita phalloides, with sodium or potassium ions in methanol. First, from the dependence of effective electrophoretic mobility of [Gly⁶ ]AA on Na⁺ or K⁺ ions concentration in the BGE (methanolic solution of 20 mM chloroacetic acid, 10 mM Tris, pH_MeOH 7.8, containing 0-50 mM NaCl or 0-40 mM KCl), the apparent binding (stability) constants of [Gly⁶ ]AA-Na⁺ and [Gly⁶ ]AA-K⁺ complexes were evaluated as 26 ± 1 and 14 ± 1 L/mol, respectively. The employed ACE method included correction of the effective mobilities measured at ambient temperature and at variable ionic strength of the BGEs to the mobilities related to the reference temperature 25°C and to the constant ionic strength 10 mM. Second, the interaction energies of the [Gly⁶ ]AA-Na⁺ and [Gly⁶ ]AA-K⁺ complexes (-466.3 and -345.2 kJ/mol, respectively) and the structural details of these complexes, such as position of the Na⁺ and K⁺ ions in the cavity of the [Gly⁶ ]AA molecule and the interatomic distances within these complexes, were determined by the density functional theory calculations.