Evaluation of Ligand-Selector Interaction from Effective Diffusion Coefficient

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.

Simultaneously performing Taylor dispersion analysis with fluorimetry, photometry, and contactless conductometry at the same detection window

Taylor dispersion analysis (TDA) is a rapid and precise method for determining the hydrodynamic radius (RH) of various substances. We present a versatile TDA system with a flow-through sample injection device, two compact 3-in-1 detectors, and a high-voltage power supply. The 3D-printed detectors combine fluorimetry (FD), photometry (AD@255 nm), and contactless conductometry (C4D) in a single head, enabling simultaneous detection at one capillary window. Using bovine serum albumin (BSA) as a model analyte, we compare TDA with different detection methods. BSA labeled with fluorescein isothiocyanate (FITC) is analyzed in both pulse mode and capillary electrophoresis (CE) TDA. FD and AD detection yield similar RH values, except when FITC binds with small ions in the buffer. In phosphate buffer, C4D underestimates RH values by approximately 18 % due to BSA self-association. In Tris-based buffers, C4D values are 87%-96 % of AD values in pulse mode. With CE-TDA using Tris-CHES buffer, no statistical difference is found across all detections. The system is also applied to CE-TDA of various compounds, particularly charged saccharides. CE-TDA improves the accuracy of TDA results from C4D. We demonstrate the resolution of mixed C4D-TDA signals with assistance from FD and AD signals, successfully resolving gluconate peaks fully covered by another compound. The versatile system with 3-in-1 detection offers a powerful tool for TDA of mixtures and enhances sample throughput.

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.

Detecting the formation of human c-KIT oncogene promoter G-Quadruplex by Taylor dispersion analysis

The formation of G-quadruplex (G4) structures in oncogenic G-rich promoter regions are implicated in their biological functions, especially the inhibition of transcription. The binding of cations is thought to contribute to the stabilization of the G4 formation and competition against the duplex formation in the genomic sequence. Furthermore, it might affect the recognition of DNA-binding proteins. Therefore, measuring the interaction between G4 DNA and cations in a free solution environment is critical for evaluating G4 DNA biological functions. However, how binding to cations (K⁺ and NH₄⁺) affects the folding equilibrium of the G4 structure remains unclear. In this work, a Taylor dispersion analysis (TDA) method using a capillary electrophoresis (CE) instrument was established for the quantitative characterization of the cation-dependent G4 formation in the human c-KIT oncogene promoter region, as well as diffusivities and hydrodynamic radii of DNA variations before and after folding. Our results showed that both K⁺ and NH₄⁺ can induce the random-coiled c-KIT DNA to unfold and form a more unstretched intermediate state and then fold into tightly structured G4s with smaller size. The G4 size induced by NH₄⁺ was smaller than that induced by K⁺ ions, though these two cations induced the c-KIT G4 DNA formation with similar binding constants (order of magnitude around 10⁶ M^-1). The TDA method can be widely used for rapid structural analyses of trace amounts of DNA mixtures, which effectively differentiate DNA variations or DNA-ligand complex conformations.

Antigen-Adjuvant Interactions in Vaccines by Taylor Dispersion Analysis: Size Characterization and Binding Parameters

Vaccine adjuvants are immunostimulatory substances used to improve and modulate the immune response induced by antigens. A better understanding of the antigen-adjuvant interactions is necessary to develop future effective vaccine. In this study, Taylor dispersion analysis (TDA) was successfully implemented to characterize the interactions between a polymeric adjuvant (poly(acrylic acid), SPA09) and a vaccine antigen in development for the treatment of Staphylococcus aureus. TDA allowed one to rapidly determine both (i) the size of the antigen-adjuvant complexes under physiological conditions and (ii) the percentage of free antigen in the adjuvant/antigen mixture at equilibrium and finally get the interaction parameters (stoichiometry and binding constant). The complex sizes obtained by TDA were compared to the results obtained by transmission electron microscopy, and the binding parameters were compared to results previously obtained by frontal analysis continuous capillary electrophoresis.

Microfluidics and the quantification of biomolecular interactions

Microfluidic systems under laminar flow conditions provide in-solution information about species size and binding affinities at very modest sample costs. Flow-induced dispersion analysis directly measures the spread of the analyte profile using Taylor dispersion analysis, whereas microfluidic diffusional sizing quantifies the transfer of analyte from one phase to another. Species of sizes between 0.5 and 1000 nm can be analyzed, and different populations resolved. Both techniques also allow analysis in complex media and medium throughput analysis. These properties make them valuable complements to existing approaches to measure biomolecular interactions.

Toward an automated workflow for the study of plasma protein-drug interactions based on capillary electrophoresis-frontal analysis combined with in-capillary mixing of interacting partners

Capillary electrophoresis-frontal analysis (CE-FA) together with mobility shift affinity CE is the most frequently used mode of affinity CE for a study of plasma protein-drug interactions, which is a substantial part of the early stage of drug discovery. Whereas in the classic CE-FA setup the sample is prepared by off-line mixing of the interaction partners in the sample vial outside the CE instrument and after a short incubation period loaded into the capillary and analysed, in this work a new methodological approach has been developed that combines CE-FA with the mixing of interacting partners directly inside the capillary. This combination gives rise to a fully automated and versatile methodology for the characterization of these binding interactions besides a substantial reduction in the amounts of sample compounds used. The minimization of possible experimental errors due to the full involving of sophisticated CE instrument in the injection procedure, mixing and separation instead of manual manipulation is another fundamental benefit. The in-capillary mixing is based on the transverse diffusion of laminar flow profile methodology introduced by Krylov et al. using its multi-zone injection modification presented by Řemínek at al.. Actually, after the method optimization, the alternate introduction of six plugs of drug and six plugs of bovine serum protein in BGE, each injected for 3 s at a pressure of -10 mbar (-1 kPa) into the capillary filled by BGE, was found to be the best injection procedure. The method repeatability calculated as RSDs of plateau highs of bovine serum albumin and propranolol as model sample compounds were better than 3.44 %. Its applicability was finally demonstrated on the determination of apparent binding parameters of bovine serum albumin for basic drugs propranolol and lidocaine and acid drug phenylbutazone. The values obtained by a new on-line CE-FA methodology are in agreement with values estimated by classic off-line CE-FA, as well as with literature data obtained using different techniques.

Kinetic Analysis of 4-Nitrophenol Reduction by "Water-Soluble" Palladium Nanoparticles

The most important model catalytic reaction to test the catalytic activity of metal nanoparticles is the reduction of 4-nitrophenol to 4-aminophenol by sodium borohydride as it can be precisely monitored by UV–vis spectroscopy with high accuracy. This work presents the catalytic reduction of 4-nitrophenol (4-Nip) to 4-aminophenol (4-Amp) in the presence of Pd nanoparticles and sodium borohydride as reductants in water. We first evaluate the kinetics using classical pseudo first-order kinetics. We report the effects of different initial 4-Nip and NaBH₄ concentrations, reaction temperatures, and mass of Pd nanoparticles used for catalytic reduction. The thermodynamic parameters (activation energy, enthalpy, and entropy) were also determined. Results show that the kinetics are highly dependent on the reactant ratio and that pseudo first-order simplification is not always fit to describe the kinetics of the reaction. Assuming that all steps of this reaction proceed only on the surface of Pd nanoparticles, we applied a Langmuir−Hinshelwood model to describe the kinetics of the reaction. Experimental data of the decay rate of 4-nitrophenol were successfully fitted to the theoretical values obtained from the Langmuir–Hinshelwood model and all thermodynamic parameters, the true rate constant k, as well as the adsorption constants of 4-Nip, and BH₄⁻ (K_4-Nip and K_BH4−) were determined for each temperature.

Transient Incomplete Separation Facilitates Finding Accurate Equilibrium Dissociation Constant of Protein-Small Molecule Complex

Current practical methods for finding the equilibrium dissociation constant, K_d , of protein-small molecule complexes have inherent sources of inaccuracy. Introduced here is "accurate constant via transient incomplete separation" (ACTIS), which appears to be free of inherent sources of inaccuracy. Conceptually, a short plug of the pre-equilibrated protein-small molecule mixture is pressure-propagated in a capillary, causing fast transient incomplete separation of the complex from the unbound small molecule. A superposition of signals from these two components is measured near the capillary exit and used to calculate a fraction of unbound small molecule, which, in turn, is used to calculate K_d . Herein the validity of ACTIS is proven theoretically, its accuracy is verified by computer simulation, and its practical use is demonstrated. ACTIS has the potential to become a reference-standard method for determining K_d  values of protein-small molecule complexes.

Nanoscopic Approach to Quantification of Equilibrium and Rate Constants of Complex Formation at Single-Molecule Level

Equilibrium and rate constants are key descriptors of complex-formation processes in a variety of chemical and biological reactions. However, these parameters are difficult to quantify, especially in the locally confined, heterogeneous, and dynamically changing living matter. Herein, we address this challenge by combining stimulated emission depletion (STED) nanoscopy with fluorescence correlation spectroscopy (FCS). STED reduces the length-scale of observation to tens of nanometres (2D)/attoliters (3D) and the time-scale to microseconds, with direct, gradual control. This allows one to distinguish diffusional and binding processes of complex-formation, even at reaction rates higher by an order of magnitude than in confocal FCS. We provide analytical autocorrelation formulas for probes undergoing diffusion-reaction processes under STED condition. We support the theoretical analysis of experimental STED-FCS data on a model system of dye-micelle, where we retrieve the equilibrium and rates constants. Our work paves a promising way toward quantitative characterization of molecular interactions in vivo.

Synergistic Effects of Gold-Palladium Nanoalloys and Reducible Supports on the Catalytic Reduction of 4-Nitrophenol

Herein we report on the catalytic activity of mesoporous nickel, iron, cerium, cobalt, and manganese oxides prepared using KIT-6 as a hard template via evaporation-assisted precipitation. The mesoporous metal oxides (MMOs) were characterized and used as heterogeneous catalysts in the reduction of 4-nitrophenol (4-Nip) by sodium borohydride (BH₄^-). Furthermore, polyamidoamide (PAMAM) dendrimers were used to synthesize gold-palladium nanoalloy particles. The size of AuPd/PAMAM was found to be 3.5 ± 0.8 nm in diameter before being immobilized on the aforementioned mesoporous metal oxides and used as catalysts in the reduction of 4-Nip. Prior to catalytic evaluation, the reduction profiles of the mesoporous metal oxides were investigated by hydrogen-temperature-programmed reduction (H₂-TPR) and showed that mesoporous metal oxides can be easily reduced at lower temperatures and that the immobilization of gold-palladium nanoalloy particles lowers their reduction temperatures. Mesoporous cobalt and manganese oxides showed catalytic activity toward 4-Nip reduction, and the activity was enhanced after immobilization of the gold-palladium nanoalloys. Isolation of nanoparticles activity was achieved by immobilization of the gold-palladium nanoalloys on the inert silica support. From this we postulated an electron relay mechanism for the reduction of 4-nitrophenol. With the use of power rate law we showed that 4-Nip reduction follows pseudo-first-order kinetics.

Analytical form of the autocorrelation function for the fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) can provide information about diffusion coefficients and rate constants of chemical reactions in small systems of interacting molecules. However, the interpretation of FCS experiments depends crucially on the model of the autocorrelation function for the fluorescence intensity fluctuations. In this theoretical work, we consider a system of fluorescent molecules that diffuse and interact with massive particles, e.g. surfactant micelles. Using the general formalism of FCS, we derive a new analytical approximation of the autocorrelation function for systems in which both diffusion and a binary reaction occur. This approximation provides a smooth interpolation between the limit of fast reaction (much faster than diffusion), and the opposite limit of slow reaction. Our studies of noncovalent interactions of micelles with dyes by FCS provided an experimental case to which the approximate autocorrelation function was successfully applied [X. Zhang, A. Poniewierski, A. Jelińska, A. Zagożdżon, A. Wisniewska, S. Hou and R. Hołyst, Soft Matter, 2016, 12, 8186-8194].

Determination of equilibrium and rate constants for complex formation by fluorescence correlation spectroscopy supplemented by dynamic light scattering and Taylor dispersion analysis

The equilibrium and rate constants of molecular complex formation are of great interest both in the field of chemistry and biology. Here, we use fluorescence correlation spectroscopy (FCS), supplemented by dynamic light scattering (DLS) and Taylor dispersion analysis (TDA), to study the complex formation in model systems of dye-micelle interactions. In our case, dyes rhodamine 110 and ATTO-488 interact with three differently charged surfactant micelles: octaethylene glycol monododecyl ether C₁₂E₈ (neutral), cetyltrimethylammonium chloride CTAC (positive) and sodium dodecyl sulfate SDS (negative). To determine the rate constants for the dye-micelle complex formation we fit the experimental data obtained by FCS with a new form of the autocorrelation function, derived in the accompanying paper. Our results show that the association rate constants for the model systems are roughly two orders of magnitude smaller than those in the case of the diffusion-controlled limit. Because the complex stability is determined by the dissociation rate constant, a two-step reaction mechanism, including the diffusion-controlled and reaction-controlled rates, is used to explain the dye-micelle interaction. In the limit of fast reaction, we apply FCS to determine the equilibrium constant from the effective diffusion coefficient of the fluorescent components. Depending on the value of the equilibrium constant, we distinguish three types of interaction in the studied systems: weak, intermediate and strong. The values of the equilibrium constant obtained from the FCS and TDA experiments are very close to each other, which supports the theoretical model used to interpret the FCS data.

Motion of Molecular Probes and Viscosity Scaling in Polyelectrolyte Solutions at Physiological Ionic Strength

We investigate transport properties of model polyelectrolyte systems at physiological ionic strength (0.154 M). Covering a broad range of flow length scales-from diffusion of molecular probes to macroscopic viscous flow-we establish a single, continuous function describing the scale dependent viscosity of high-salt polyelectrolyte solutions. The data are consistent with the model developed previously for electrically neutral polymers in a good solvent. The presented approach merges the power-law scaling concepts of de Gennes with the idea of exponential length scale dependence of effective viscosity in complex liquids. The result is a simple and applicable description of transport properties of high-salt polyelectrolyte solutions at all length scales, valid for motion of single molecules as well as macroscopic flow of the complex liquid.

Flow induced dispersion analysis rapidly quantifies proteins in human plasma samples

Rapid and sensitive quantification of protein based biomarkers and drugs is a substantial challenge in diagnostics and biopharmaceutical drug development. Current technologies, such as ELISA, are characterized by being slow (hours), requiring relatively large amounts of sample and being subject to cumbersome and expensive assay development. In this work a new approach for quantification based on changes in diffusivity is presented. The apparent diffusivity of an indicator molecule interacting with the protein of interest is determined by Taylor Dispersion Analysis (TDA) in a hydrodynamic flow system. In the presence of the analyte the apparent diffusivity of the indicator changes due to complexation. This change in diffusivity is used to quantify the analyte. This approach, termed Flow Induced Dispersion Analysis (FIDA), is characterized by being fast (minutes), selective (quantification is possible in a blood plasma matrix), fully automated, and being subject to a simple assay development. FIDA is demonstrated for quantification of the protein Human Serum Albumin (HSA) in human plasma as well as for quantification of an antibody against HSA. The sensitivity of the FIDA assay depends on the indicator-analyte dissociation constant which in favourable cases is in the sub-nanomolar to picomolar range for antibody-antigen interactions.

Preparation of well-defined dendrimer encapsulated ruthenium nanoparticles and their evaluation in the reduction of 4-nitrophenol according to the Langmuir-Hinshelwood approach

This study discusses the preparation of various sized dendrimer encapsulated ruthenium nanoparticles (RuDEN) with the use of the generation 4 (G4), generation 5 (G5), and generation 6 (G6) hydroxyl-terminated poly(amidoamine) (PAMAM-OH) dendrimers as templating agents. The size of the nanoparticles ranges from 1.1 to 2.2 nm. These catalysts were fully characterized using UV/vis spectrophotometry, infrared (IR) spectroscopy, and transmission electron microscopy (TEM). The RuDEN catalysts were evaluated in the reduction of 4-nitrophenol (4NP) in the presence of sodium borohydride (BH4(-)) for various concentrations of either. The kinetic data obtained were modeled to the Langmuir-Hinshelwood equation. The model allows the relation of the apparent rate constant to the total surface area S of the nanoparticle, the kinetic constant k which is related to the rate-determining step, and the adsorption constants K(4NP) and K(BH4) for 4NP and borohydride, respectively. These parameters were calculated for each of the RuDENs, proving the Langmuir-Hinshelwood model to be suitable for the kinetic evaluation of RuDENs in the catalytic reduction of 4NP.