Kinetic CE: foundation for homogeneous kinetic affinity methods

Deterministic error propagation in ITC: Revealing multi-fold errors in Kd values under standard conditions

Accurate determination of the equilibrium dissociation constant (Kd) is essential in fields such as drug discovery and molecular diagnostics, where a rigorous understanding of molecular interactions drives critical decisions. Among established techniques, isothermal titration calorimetry (ITC) is highly valued for its ability to directly capture binding thermodynamics without the need for labeling or immobilization. However, while ITC is often praised for its precision, potential inaccuracies due to the systematic errors in experimental variables (analyte concentrations and measured heat) are frequently overlooked. One key reason for this oversight is the lack of a deterministic framework that explicitly demonstrates how ITC-derived Kd values can be affected by these errors. To address this gap, we derived a closed-form mathematical model for error propagation in ITC-based Kd determination, quantifying the impact of inaccuracies in analyte concentrations and measured heat on the resulting Kd. This framework provides a robust foundation for understanding and predicting the influence of these systematic errors on Kd accuracy. Using this solution, we demonstrate that even within the conventionally recommended c-value range of 10-100, expected systematic errors in concentrations and heat can potentially lead to significant multi-fold deviations in Kd. These findings underscore the need for quantitative accuracy assessments in ITC experiments and highlight the importance of developing practical tools to support such evaluations.

From non-affinity to high-affinity: Rapid preparation of nanobodies utilizing high-precision alphafold and structural-interaction analysis for detection of enrofloxacin in marine fish

Traditional antibody preparation methods rely on animal immunization and experimental screening, often requiring 3-6 months, which cannot meet the urgent demands for antibodies in environmental emergencies or contamination events. Herein, a rapid antibody preparation method was proposed to transform anti-macromolecule nanobodies into high-affinity anti-small molecule (enrofloxacin) nanobodies, based on the high-precision predictive capabilities of AlphaFold, integrated with structural and interaction analysis. The high-precision prediction capability of AlphaFold ensured the accuracy of nanobody structural analysis and targeted modification. Binding structure design enabled the antigen and antibody to adopt an optimal binding conformation. Interaction analysis provided guidance for targeted modifications and served as a tool for evaluating the results. Molecular docking results revealed that the template nanobodies, which initially couldn't dock with enrofloxacin, formed 3-5 noncovalent bonds after modification. Bio-layer interferometry (BLI) assays demonstrated that the equilibrium dissociation constant (KD) of the modified nanobodies ranged from 5.56 ± 0.34 nM to 94.73 ± 4.35 nM, with half-maximal inhibitory concentration (IC50) between 231.9 and 3293.6 ng/mL. Based on the modified nanobodies and BLI platform, the detection of enrofloxacin in marine fish was achieved with a limit of detection (LOD) as low as 59.97 μg/kg. In summary, this study provided a novel perspective for the rapid nanobody preparation, showing significant potential in food safety and environmental monitoring.

Maximizing the Accuracy of Equilibrium Dissociation Constants for Affinity Complexes: From Theory to Practical Recommendations

The equilibrium dissociation constant (Kd) is a major characteristic of affinity complexes and one of the most frequently determined physicochemical parameters. Despite its significance, the values of Kd obtained for the same complex under similar conditions often exhibit considerable discrepancies and sometimes vary by orders of magnitude. These inconsistencies highlight the susceptibility of Kd determination to large systematic errors, even when random errors are small. It is imperative to both minimize and quantitatively assess the systematic errors inherent in Kd determination. Traditionally, Kd values are determined through nonlinear regression of binding isotherms. This analysis utilizes three variables: concentrations of two reactants and a fraction R of unbound limiting reactant. The systematic errors in Kd arise directly from systematic errors in these variables. Therefore, to maximize the accuracy of Kd, this study thoroughly analyzes the sources of systematic errors within the three variables, including (i) non-additive signals to calculate R, (ii) mis-calibrated experimental instruments, (iii) inaccurate calibration parameters, (iv) insufficient incubation time, (v) unsaturated binding isotherm, (vi) impurities in the reactants, and (vii) solute adsorption onto surfaces. Through this analysis, we illustrate how each source contributes to inaccuracies in the determination of Kd and propose strategies to minimize these contributions. Additionally, we introduce a method for quantitatively assessing the confidence intervals of systematic errors in concentrations, a crucial step toward quantitatively evaluating the accuracy of Kd. While presenting original findings, this paper also reiterates the fundamentals of Kd determination, hence guiding researchers across all proficiency levels. By shedding light on the sources of systematic errors and offering strategies for their mitigation, our work will help researchers enhance the accuracy of Kd determination, thereby making binding studies more reliable and the conclusions drawn from such studies more robust.

Atypical applications of transverse diffusion of laminar flow profiles methodology for in-capillary reactions in capillary electrophoresis

Capillary electrophoresis (CE) is a powerful separation technique offering quick and efficient analyses in various fields of bioanalytical chemistry. It is characterized by many well-known advantages, but one, which is perhaps the most important for this application field, is somewhat overlooked. It is the possibility to perform chemical and biochemical reactions at the nL scale inside the separation capillary. There are two basic formats applicable for this purpose, heterogeneous and homogeneous. In the former, one reactant is immobilized onto a particle or monolithic support or directly on the capillary wall, and the other is injected. In the latter, the reactant mixing inside a capillary is based on electromigration or diffusion. One of the diffusion-based methodologies, termed Transverse Diffusion of Laminar Flow Profiles, is the subject of this review. Since most studies utilizing in-capillary reactions in CE focus on enzymes, which are being continuously and exhaustively reviewed, this review covers the atypical applications of this methodology, but still in the bioanalytical field. As can be seen from the demonstrated applications, they are not limited to reactions, but can also be utilized for other biochemical systems.

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.

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.

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.

Comparative analysis of aptamers binding to SARS-CoV-2 N protein using capillary electrophoresis and bio-layer interferometry

Aptamers are increasingly employed in SARS-CoV-2 theragnostics in recent years. Characterization of aptamers, testing affinity and kinetic parameters (e.g., equilibrium dissociation constant (KD), kon, and koff), can be done by several methods and influenced by many factors. This study aims to characterize the binding of aptamers to SARS-CoV-2 nucleocapsid (N) protein using capillary electrophoresis (CE) and bio-layer interferometry (BLI). These two analytical methods differ by how the aptamer binds to its target protein once the aptamer, as a capture ligand, is partitioned in solution (CE) or immobilized on the biosensor (BLI). With CE, the KD values of the N-binding aptamers (tNSP1, tNSP2, and tNSP3) were determined to be 18 ± 4 nM, 45 ± 11 nM, and 32 ± 7 nM, respectively, while the KD measurements by BLI yielded 4.8 ± 0.6, 4.5 ± 0.5, and 2.9 ± 0.3 nM, respectively. CE results showed a higher KD across all aptamers tested. The differences in the steric hindrance and confirmational structures of the aptamers immobilized on the BLI biosensors versus those suspended in the CE sample solution affect the molecular interactions between aptamers and the target proteins. Moreover, the buffer composition including pH and ionic strength can influence the stability of aptamer structures, or aptamer-protein complexes. All these variables affect the binding and calculated KD. In this sense, a KD value alone is not sufficient to make comparisons between aptamers; instead, the entire experimental setup should also be considered. This is particularly important when implementing aptamers in different bioanalytical systems.

Induction of binding sites for RecA aptamers by differentiated-competition capillary Electrophoresis-SELEX

The binding site-oriented SELEX strategy is an effective way to promote the functional evolution of aptamers. Here we report a novel aptamer screening strategy (Differentiated-competition Capillary Electrophoresis-SELEX), which enables candidate aptamers to be directionally induced to bind to different active sites of RecA. In this strategy, we introduce two competing binding factors into the "binding - dissociation" dynamic equilibrium system of RecA and ssDNA libraries. Due to the completely different binding mechanism of the competitive factor and the ssDNA library, it exerts different interference on the binding of RecA and the ssDNA library, which directed the binding site of aptamer candidates during the SELEX process. Multifunctional aptamers with high affinity and specificity were found to inhibit RecA activity by binding to different active sites. In conclusion, the SELEX method developed in our current study have identified a variety of biologically functional aptamers with relatively well-defined binding sites that regulate RecA protein activity, which has potential applications and future prospects for accurate screening of biological functional aptamers.

Study of molecular interactions by nonequilibrium capillary electrophoresis of equilibrium mixtures: Originations, developments, and applications

Molecular interactions play a vital role in regulating various physiological and biochemical processes in vivo. Kinetic capillary electrophoresis (KCE) is an analytical platform that offers significant advantages in studying the thermodynamic and kinetic parameters of molecular interactions. It enables the simultaneous analysis of these parameters within an interaction pattern and facilitates the screening of binding ligands with predetermined kinetic parameters. Nonequilibrium capillary electrophoresis of equilibrium mixtures (NECEEM) was the first proposed KCE method, and it has found widespread use in studying molecular interactions involving proteins/aptamers, proteins/small molecules, and peptides/small molecules. The successful applications of NECEEM have demonstrated its promising potential for further development and broader application. However, there has been a dearth of recent reviews on NECEEM. To address this gap, our study provides a comprehensive description of NECEEM, encompassing its origins, development, and applications from 2015 to 2022. The primary focus of the applications section is on aptamer selection and screening of small-molecule ligands. Furthermore, we discuss important considerations in NECEEM experimental design, such as buffer suitability, detector selection, and protein adsorption. By offering this thorough review, we aim to contribute to the understanding, advancement, and wider utilization of NECEEM as a valuable tool for studying molecular interactions and facilitating the identification of potential ligands and targets.

Strategies for capillary electrophoresis: Method development and validation for pharmaceutical and biological applications-Updated and completely revised edition

This review is in support of the development of selective, precise, fast, and validated capillary electrophoresis (CE) methods. It follows up a similar article from 1998, Wätzig H, Degenhardt M, Kunkel A. "Strategies for capillary electrophoresis: method development and validation for pharmaceutical and biological applications," pointing out which fundamentals are still valid and at the same time showing the enormous achievements in the last 25 years. The structures of both reviews are widely similar, in order to facilitate their simultaneous use. Focusing on pharmaceutical and biological applications, the successful use of CE is now demonstrated by more than 600 carefully selected references. Many of those are recent reviews; therefore, a significant overview about the field is provided. There are extra sections about sample pretreatment related to CE and microchip CE, and a completely revised section about method development for protein analytes and biomolecules in general. The general strategies for method development are summed up with regard to selectivity, efficiency, precision, analysis time, limit of detection, sample pretreatment requirements, and validation.

Vanadium(IV) and vanadium(V) complexation by succinic acid studied by affinity capillary electrophoresis. Simultaneous injection of two analytes in equilibrium studies

The interaction of V(IV) and V(V) with succinic acid was investigated by affinity capillary electrophoresis (ACE) in aqueous acid solutions at pH values 1.5, 2.0 and 2.4, and different ligand concentrations. V(IV) and V(V) form protonated complexes with succinic acid ligand at this pH range. The logarithms of the stability constants, measured at 0.1 mol L^-1 (NaClO₄/HClO₄) ionic strength and 25 °C, are logβ₁₁₁=7.4 ± 0.2 and logβ₁₂₂=14.1 ± 0.5 for V(IV), and logβ₁₁₁=7.3 ± 0.1 for V(V), respectively. The stability constant values, extrapolated to zero ionic strength with the Davies equation, are logβ°₁₁₁=8.3 ± 0.2 and logβ°₁₂₂=15.6 ± 0.5 for V(IV) and logβ°₁₁₁=7.9 ± 0.1 for V(V). The application of ACE to the simultaneous equilibria of V(IV) and V(V) (injection of two analytes) was also attempted. When the results were compared with those obtained when introducing only one analyte in the capillary, using the traditional version of the method, similar stability constants and precision are obtained. The possibility of studying two analytes simultaneously decreases the time needed for the determination of the constants; this feature is especially valuable when working with hazardous materials or when only small quantities of ligand are available.

Analysis of drug interactions with serum proteins and related binding agents by affinity capillary electrophoresis: A review

Biomolecules such as serum proteins can interact with drugs in the body and influence their pharmaceutical effects. Specific and precise methods that analyze these interactions are critical for drug development or monitoring and for diagnostic purposes. Affinity capillary electrophoresis (ACE) is one technique that can be used to examine the binding between drugs and serum proteins, or other agents found in serum or blood. This article will review the basic principles of ACE, along with related affinity-based capillary electrophoresis (CE) methods, and examine recent developments that have occurred in this field as related to the characterization of drug-protein interactions. An overview will be given of the various formats that can be used in ACE and CE for such work, including the relative advantages or weaknesses of each approach. Various applications of ACE and affinity-based CE methods for the analysis of drug interactions with serum proteins and other binding agents will also be presented. Applications of ACE and related techniques that will be discussed include drug interaction studies with serum agents, chiral drug separations employing serum proteins, and the use of CE in hybrid methods to characterize drug binding with serum proteins.

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.

Capillary electrophoresis-based methodology for screening of oligonucleotide aptamers

As a new molecular recognition element, oligonucleotide aptamer not only has higher affinity and specificity to target molecules, but also has the advantages of wide recognition range, in vitro synthesis and chemical stability compared with conventional antibodies. Since a kind of screening method termed systematic evolution of ligands by exponential enrichment (SELEX) was reported, scientists have extensively researched the methodology of how to highly and efficiently screen out aptamers from a library consisting of a large number of random oligonucleotides. Certainly capillary electrophoresis-based screening methodologies, including nonequilibrium capillary electrophoresis of equilibrium mixtures, equilibrium capillary electrophoresis of equilibrium mixtures, non-SELEX, ideal-filter capillary electrophoresis, capillary transient isotachophoresis, etc., are revolutionary. Compared with conventional SELEX, these capillary electrophoresis-based methodologies show incomparable advantages such as the single-round screening of aptamers and increased successful screening rate. Methodology studies on the screening process of aptamers are comprehensively reviewed.

How to Develop and Prove High-Efficiency Selection of Ligands from Oligonucleotide Libraries: A Universal Framework for Aptamers and DNA-Encoded Small-Molecule Ligands

Screening molecular libraries for ligands capable of binding proteins is widely used for hit identification in the early drug discovery process. Oligonucleotide libraries provide a very high diversity of compounds, while the combination of the polymerase chain reaction and DNA sequencing allow the identification of ligands in low copy numbers selected from such libraries. Ligand selection from oligonucleotide libraries requires mixing the library with the target followed by the physical separation of the ligand-target complexes from the unbound library. Cumulatively, the low abundance of ligands in the library and the low efficiency of available separation methods necessitate multiple consecutive rounds of partitioning. Multiple rounds of inefficient partitioning make the selection process ineffective and prone to failures. There are continuing efforts to develop a separation method capable of reliably generating a pure pool of ligands in a single round of partitioning; however, none of the proposed methods for single-round selection have been universally adopted. Our analysis revealed that the developers' efforts are disconnected from each other and hindered by the lack of quantitative criteria of selection quality assessment. Here, we present a formalism that describes single-round selection mathematically and provides parameters for quantitative characterization of selection quality. We use this formalism to define a universal strategy for development and validation of single-round selection methods. Finally, we analyze the existing partitioning methods, the published single-round selection reports, and some pertinent practical considerations through the prism of this formalism. This formalism is not an experimental protocol but a framework for correct development of experimental protocols. While single-round selection is not a goal by itself and may not always suffice selection of good-quality ligands, our work will help developers of highly efficient selection approaches to consolidate their efforts under an umbrella of universal quantitative criteria of method development and assessment.

Rapid electrotransfer probing for improved detection sensitivity in in-gel immunoassays

Protein electrotransfer in conventional western blotting facilitates detection of size-separated proteins by diffusive immunoprobing, as analytes are transferred from a small-pore sizing gel to a blotting membrane for detection. This additional transfer step can, however, impair detection sensitivity through protein losses and confound protein localization. To overcome challenges associated with protein transfer, in-gel immunoassays immobilize target proteins to the hydrogel matrix for subsequent in-gel immunoprobing. Yet, detection sensitivity in diffusive immunoprobing of hydrogels is determined by the gel pore size relative to the probe size, and in-gel immunoprobing results in (i) reduced in-gel probe concentration compared to surrounding free-solution, and (ii) slow in-gel probe transfer compared to immunocomplex dissociation. Here, we demonstrate electrotransfer probing for effective and rapid immunoprobing of in-gel immunoassays. Critically, probe (rather than target protein) is electrotransferred from an inert, large-pore 'loading gel' to a small-pore protein sizing gel. Electric field is used as a tuneable parameter for electromigration velocity, providing electrotransfer probing with a fundamental advantage over diffusive probing. Using electrotransfer probing, we observe 6.5 ± 0.1× greater probe concentration loaded in-gel in ∼82× time reduction, and 2.7 ± 0.4× less probe concentration remaining in-gel after unloading in ∼180× time reduction (compared to diffusive probing). We then apply electrotransfer probing to detect OVA immobilized in-gel and achieve 4.1 ± 3.4× greater signal-to-noise ratio and 30× reduction in total immunoprobing duration compared to diffusive probing. We demonstrate electrotransfer probing as a substantially faster immunoprobing method for improved detection sensitivity of protein sizing in-gel immunoassays.

Kinetic Analysis by Affinity Chromatography

Important information on chemical processes in living systems can be obtained by the rates at which these biological interactions occur. This review will discuss several techniques based on traditional and high-performance affinity chromatography that may be used to examine the kinetics of biological reactions. These methods include band-broadening measurements, techniques for peak fitting, split-peak analysis, peak decay studies, and ultrafast affinity extraction. The general principles and theory of each method, as applied to the determination of rate constants, will be discussed. The applications of each approach, along with its advantages and limitations, will also be considered.

Capillary electrophoresis-based approaches for the study of affinity interactions combined with various sensitive and nontraditional detection techniques

Nearly all processes in living organisms are controlled and regulated by the synergy of many biomolecule interactions involving proteins, peptides, nucleic acids, nucleotides, saccharides, and small molecular weight ligands. There is growing interest in understanding them, not only for the purposes of interactomics as an essential part of system biology, but also in their further elucidation in disease pathology, diagnostics, and treatment. The necessity of detailed investigation of these interactions leads to the requirement of laboratory methods characterized by high efficiency and sensitivity. As a result, many instrumental approaches differing in their fundamental principles have been developed, including those based on capillary electrophoresis. Although capillary electrophoresis offers numerous advantages for such studies, it still has one serious limitation, its poor concentration sensitivity with the most commonly used detection method-ultraviolet-visible spectrometry. However, coupling capillary electrophoresis with a more sensitive detector fulfils the above-mentioned requirement. In this review, capillary electrophoresis combined with fluorescence, mass spectrometry, and several nontraditional detection techniques in affinity interaction studies are summarized and discussed, together with the possibility of conducting these measurements in microchip format.

Moment analysis for mass transfer kinetics at the interface of spherical molecular aggregates

New moment equations were developed on the basis of the principle of relativity for explaining some characteristics of elution peaks measured by electrokinetic chromatography (EKC) using spherical molecular aggregates. Basic equations representing mass balance and mass transfer kinetics in EKC 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 EKC 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 EKC peaks in S were derived from those in S' by the inverse Galilean transformation. The moment equations were used to the re-analysis of EKC data previously measured. The values of permeation rate constants of thymol at the interface of sodium dodecylsulfate micelles were fairly in agreement with those determined in a previous study. The moment equations were also used to the numerical simulation of elution peaks in EKC systems. The influence of some experimental parameters on elution peak profiles was quantitatively analyzed. The moment equations are useful for determining the rate constants of interfacial solute permeation from elution peak profiles measured by EKC.

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.

Mathematical Modeling of Bioassays

The high affinity and specificity of biological receptors determine the demand for and the intensive development of analytical systems based on use of these receptors. Therefore, theoretical concepts of the mechanisms of these systems, quantitative parameters of their reactions, and relationships between their characteristics and ligand-receptor interactions have become extremely important. Many mathematical models describing different bioassay formats have been proposed. However, there is almost no information on the comparative characteristics of these models, their assumptions, and predictive insights. In this review we suggested a set of criteria to classify various bioassays and reviewed classical and contemporary publications on these bioassays with special emphasis on immunochemical analysis systems as the most common and in-demand techniques. The possibilities of analytical and numerical modeling are discussed, as well as estimations of the minimum concentrations that may be detected in bioassays and recommendations for the choice of assay conditions.

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).

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.

Aptamers as Valuable Molecular Tools in Neurosciences

Aptamers are short nucleic acids that interact with a variety of targets with high affinity and specificity. They have been shown to inhibit biological functions of cognate target proteins, and they are identifiable by an in vitro selection process, also termed SELEX (Systematic Evolution of Ligands by EXponential enrichment). Being nucleic acids, aptamers can be synthesized chemically or enzymatically. The latter renders RNA aptamers compatible with the cell's own transcription machinery and, thus, expressable inside cells. The synthesis of aptamers by chemical approaches opens up the possibility of producing aptamers on a large scale and enables a straightforward access to introduce modifications in a site-specific manner (e.g., fluorophores or photo-labile groups). These characteristics make aptamers broadly applicable (e.g., as an analytical, diagnostic, or separation tool). In this TechSight, we provide a brief overview on aptamer technology and the potential of aptamers as valuable research tools in neurosciences.

Synthetic, Switchable Enzymes

The construction of switchable, radiation-controlled, aptameric enzymes - "swenzymes" - is, in principle, feasible. We propose a strategy to make such catalysts from 2 (or more) aptamers each selected to bind specifically to one of the substrates in, for example, a 2-substrate reaction. Construction of a combinatorial library of candidate swenzymes entails selecting a set of a million aptamers that bind one substrate and a second set of a million aptamers that bind the second substrate; the aptamers in these sets are then linked pairwise by a linker, thus bringing together the substrates. In the presence of the substrates, some linked aptamer pairs catalyze the reaction when exposed to external energy in the form of a specific frequency of low-intensity, nonionizing electromagnetic or acoustic radiation. Such swenzymes are detected via a separate product-capturing aptamer that changes conformation on capturing the product; this altered conformation allows it (1) to bind to every potential swenzyme in its vicinity (thereby giving a higher probability of capture to the swenzymes that generate the product) and (2) to bind to a sequence on a magnetic bead (thereby permitting purification of the swenzyme plus product-capturing aptamer by precipitation). Attempts to implement the swenzyme strategy may help elucidate fundamental problems in enzyme catalysis.

Determination of equilibrium dissociation constants for recombinant antibodies by high-throughput affinity electrophoresis

High-quality immunoreagents enhance the performance and reproducibility of immunoassays and, in turn, the quality of both biological and clinical measurements. High quality recombinant immunoreagents are generated using antibody-phage display. One metric of antibody quality – the binding affinity – is quantified through the dissociation constant (K_D) of each recombinant antibody and the target antigen. To characterize the K_D of recombinant antibodies and target antigen, we introduce affinity electrophoretic mobility shift assays (EMSAs) in a high-throughput format suitable for small volume samples. A microfluidic card comprised of free-standing polyacrylamide gel (fsPAG) separation lanes supports 384 concurrent EMSAs in 30 s using a single power source. Sample is dispensed onto the microfluidic EMSA card by acoustic droplet ejection (ADE), which reduces EMSA variability compared to sample dispensing using manual or pin tools. The K_D for each of a six-member fragment antigen-binding fragment library is reported using ~25-fold less sample mass and ~5-fold less time than conventional heterogeneous assays. Given the form factor and performance of this micro- and mesofluidic workflow, we have developed a sample-sparing, high-throughput, solution-phase alternative for biomolecular affinity characterization.

Microfluidic Platform for Assessment of Therapeutic Proteins Using Molecular Charge Modulation Enhanced Electrokinetic Concentration Assays

Therapeutic proteins (TPs) are critical in modern medicine, yet shortage of TPs in disaster situations and remote areas remains a worldwide challenge. Manufacturing and real-time release of TPs on demand at the point-of-care is considered the key to this issue, which requires reliable and rapid analytics techniques for quality assurance. Herein we report a microfluidic platform that could be implemented in-line and at the point-of-care for real-time decision-making about the quality of a TP. The in vivo efficacy and duration of efficacy of TPs were assessed by the equilibrium and kinetics of TP and TP receptor (TPR) binding, using electrokinetic concentration (EC) and molecular charge modulation (MCM). EC can simultaneously concentrate and separate bound and unbound species in an assay based on electrical mobility, allowing for the quantification of binding. MCM enables the application of EC to arbitrary TPs by enhancing the mobility differences between TPs, TPRs, and TP-TPR complexes. This technology is homogeneous and overcomes many practical challenges of conventional heterogeneous assays. We developed various formats of assays for equilibrium and kinetic analysis and rapid determination of degradation of TPs, obtaining results comparable to state-of-the-art technologies with significantly less time (<1 h) and simpler setup. Finally, we demonstrated that the results of MCM-EC based assays correlated well with those from mass spectrometry and cell-based assay, which are the industrial standards for quality testing of TPs.

Kinetic Study of Interaction between Solute Molecule and Surfactant Micelle

We developed moment analysis of affinity kinetics by chromatographic capillary electrophoresis (MKCCE) method for the kinetic study of intermolecular interactions. Association and dissociation rate constants of the interaction in a micellar electrokinetic chromatography (MEKC) system between thymol and sodium dodecylsulfate micelle were determined by the MKCCE method. It is a method based on the moment theory for the kinetic study of intermolecular interactions under the conditions that neither immobilization nor chemical modification of molecules is required. In CCE mode, experimental conditions are controlled so that the migration of solute-micelle complex is stopped and only solute molecules migrate in a capillary. Mass transfer behavior of solute molecules in the CCE system is analogous to that in a chromatographic system. However, because it was difficult in practice to really perform CE experiments under the CCE conditions, CE data were measured with changing experimental conditions, i.e., applied pressure, under the conditions that the migration velocity of solute-micelle complex was around zero. The rate constants could be analytically determined from the CE data. In the MKCCE method, it is not necessary to fit elution curves numerically calculated to those experimentally measured for the determination of the rate constants. Regarding the interaction between thymol and SDS micelles, association equilibrium constant and association and dissociation rate constants were determined as 6.35 × 10(3) dm(3) mol(-1), 5.6 × 10(4) dm(3) mol(-1) s(-1), and 8.7 s(-1), respectively. It was demonstrated that the MKCCE method was effective for the kinetic study of intermolecular interactions.