Simple Determination of Affinity Constants of Antibodies by Competitive Immunoassays.

The affinity constant, also known as the equilibrium constant, binding constant, equilibrium association constant, or the reciprocal value, the equilibrium dissociation constant (Kd), can be considered as one of the most important characteristics for any antibody-antigen pair. Many methods based on different technologies have been proposed and used to determine this value. However, since a very large number of publications and commercial datasheets do not include this information, significant obstacles in performing such measurements seem to exist. In other cases where such data are reported, the results have often proved to be unreliable. This situation may indicate that most of the technologies available today require a high level of expertise and effort that does not seem to be available in many laboratories. In this paper, we present a simple approach based on standard immunoassay technology that is easy and quick to perform. It relies on the effect that the molar IC50 approaches the Kd value in the case of infinitely small concentrations of the reagent concentrations. A two-dimensional dilution of the reagents leads to an asymptotic convergence to Kd. The approach has some similarity to the well-known checkerboard titration used for the optimization of immunoassays. A well-known antibody against the FLAG peptide, clone M2, was used as a model system and the results were compared with other methods. This approach could be used in any case where a competitive assay is available or can be developed. The determination of an affinity constant should belong to the crucial parameters in any quality control of antibody-related products and assays and should be mandatory in papers using immunochemical protocols.

Structure and Stability of Ago2 MID-Nucleotide Complexes: All-in-One (Drop) His6-SUMO Tag Removal, Nucleotide Binding, and Crystal Growth.

The middle (MID) domain of eukaryotic Argonaute (Ago) proteins and archaeal and bacterial homologues mediates the interaction with the 5'-terminal nucleotide of miRNA and siRNA guide strands. The MID domain of human Ago2 (hAgo2) is comprised of 139 amino acids with a molecular weight of 15.56 kDa. MID adopts a Rossman-like beta1-alpha1-beta2-alpha2-beta3-alpha3-beta4-alpha4 fold with a nucleotide specificity loop between beta3 and alpha3. Multiple crystal structures of nucleotides bound to hAgo2 MID have been reported, whereby complexes were obtained by soaking ligands into crystals of MID domain alone. This protocol describes a simplified one-step approach to grow well-diffracting crystals of hAgo2 MID-nucleotide complexes by mixing purified His6-SUMO-MID fusion protein, Ulp1 protease, and excess nucleotide in the presence of buffer and precipitant. The crystal structures of MID complexes with UMP, UTP and 2'-3' linked α-L-threofuranosyl thymidine-3'-triphosphate (tTTP) are presented. This article also describes fluorescence-based assays to measure dissociation constants (Kd) of MID-nucleotide interactions for nucleoside 5'-monophosphates and nucleoside 3',5'-bisphosphates. © 2024 The Authors. Current Protocols published by Wiley Periodicals LLC. Basic Protocol 1: Crystallization of Ago2 MID-nucleotide complexes Basic Protocol 2: Measurement of dissociation constant Kd between Ago2 MID and nucleotides.

Estimating RNA Secondary Structure Folding Free Energy Changes with efn2.

A number of analyses require estimates of the folding free energy changes of specific RNA secondary structures. These predictions are often based on a set of nearest neighbor parameters that models the folding stability of a RNA secondary structure as the sum of folding stabilities of the structural elements that comprise the secondary structure. In the software suite RNAstructure, the free energy change calculation is implemented in the program efn2. The efn2 program estimates the folding free energy change and the experimental uncertainty in the folding free energy change. It can be run through the graphical user interface for RNAstructure, from the command line, or a web server. This chapter provides detailed protocols for using efn2.

Discussion on the thermodynamic calculation and adsorption spontaneity re Ofudje et al. (2023).

Accurate calculations and precise results are very important for the dissemination of scientific knowledge, whereas the errors of calculation will diminish the academic value of the paper. This discussion focuses on the calculation of thermodynamics and the determination of the spontaneity of adsorption processes in the paper of Ofudje et al. (2023). Ofudje et al. found that the apatite synthesized by chemical method (CHAp) has excellent adsorption properties for cadmium ions, which is an important contribution to the remediation of cadmium pollution. However, the calculation results of standard Gibbs free energy change (ΔGo), standard enthalpy change (ΔHo) and standard entropy change (ΔSo) of the adsorption of Cd2+ onto CHAp surface need to be corrected due to an incorrect calculation. Firstly, the partition coefficient (KD) with a dimension cannot be used for thermodynamic calculation. Secondly, the adsorbent mass (m) described by Ofudje et al. in different Sections is inconsistent, leading to incorrect results of Ko and ΔGo. When the appropriate value of the adsorbent mass is selected and the partition coefficient is converted to the standard adsorption equilibrium constant Ko, the calculated ΔGo is less than zero, which means that the adsorption is spontaneous. This discussion provides the correct calculation method of standard adsorption equilibrium constants and thermodynamic parameters, which can improve the reader's judgment and understanding of adsorption spontaneity.

Investigating the influence of solvent type and pH on protein adsorption onto silica surface by evanescent-wave cavity ring-down spectroscopy.

Several studies have explored the adsorption of various proteins onto solid-liquid interfaces, revealing the crucial role of buffer solutions in biological processes. However, a comprehensive evaluation of the buffer's influence on protein absorption onto fused silica is still lacking. This study employs evanescent-wave cavity ring-down spectroscopy (EW-CRDS) to assess the influence of buffer solutions and pH on the adsorption kinetics of three globular proteins: hemoglobin (Hb), myoglobin (Mb), and cytochrome c (Cyt-C) onto fused silica. The EW-CRDS tool, with a ring-down time of 1.4 µ s and a minimum detectable absorbance of 1 × 10 - 6 , enabled precise optical measurements at solid-liquid interfaces. The three heme proteins' adsorption behavior was investigated at pH 7 in three different solvents: deionized (DI) water, tris(hydroxymethyl)-aminomethane hydrochloride (Tris-HCl), and phosphate buffered saline (PBS). For each protein, the surface coverage, the adsorption and desorption constants, and the surface equilibrium constant were optically measured by our EW-CRDS tool. Depending on the nature of each solvent, the proteins showed a completely different adsorption trend on the silica surface. The adsorption of Mb on the silica surface was depressed in the presence of both Tris-HCl and PBS buffers compared with unbuffered (DI water) solutions. In contrast, Cyt-C adsorption appears to be relatively unaffected by the choice of buffer, as it involves strong electrostatic interactions with the surface. Notably, Hb exhibits an opposite trend, with enhanced protein adsorption in the presence of Tris-HCl and PBS buffer. The pH investigations demonstrated that the electrostatic interactions between the proteins and the surface had a major influence on protein adsorption on the silica surface, with adsorption being greatest when the pH values were around the protein's isoelectric point. This study demonstrated the ability of the highly sensitive EW-CRDS tool to study the adsorption events of the evanescent-field-confined protein species in real-time at low surface coverages with fast resolution, making it a valuable tool for studying biomolecule kinetics at solid-liquid interfaces.

Determination of binding constants by ultrafast affinity extraction: Theoretical and experimental studies of optimum conditions for analysis.

Ultrafast affinity extraction (UAE) is a form of microscale affinity HPLC that can be employed to quickly measure equilibrium constants for solute-binding agent interactions in solution. This study used chromatographic and equilibrium theory with universal plots to examine the general conditions that are needed in UAE to obtain accurate, precise, and robust measurements of equilibrium constants for such interactions. The predicted results were compared to those obtained by UAE in studies that examined the binding of various drugs with two transport proteins: human serum albumin and α1-acid glycoprotein. The most precise and robust conditions for these binding studies occurred for systems with intermediate values for their equilibrium free fraction for the solute (F0 ≈ 0.20-0.80). These trends showed good agreement with those seen in prior studies using UAE. It was further determined how the apparent free fraction of a solute was related to the dissociation rate of this solute, the time allowed for solute dissociation during UAE, and the equilibrium free fraction for the solute. These results also agreed with experimental results, as obtained for the binding of warfarin and gliclazide with human serum albumin. The final section examined how a change in the apparent free fraction, as caused by solute dissociation, affected the accuracy of an equilibrium constant that was measured by UAE. In addition, theoretical plots were generated to allow the selection of conditions for UAE that provided a given level of accuracy during the measurement of an equilibrium constant. The equations created and trends identified for UAE were general ones that can be extended in future work to other solutes and binding agents.

Recommendations for performing measurements of apparent equilibrium constants of enzyme-catalyzed reactions and for reporting the results of these measurements.

The measurement of values of apparent equilibrium constants K' for enzyme-catalyzed reactions involve a substantial number of critical details, neglect of which could lead to systematic errors. Here, interferences, impurities in the substances used, and failure to achieve equilibrium are matters of substantial consequence. Careful reporting of results is of great importance if the results are to have archival value. Thus, attention must be paid to the identification of the substances, specification of the reaction(s), the conditions of reaction, the definition of the equilibrium constant(s) and standard states, the use of standard nomenclature, symbols, and units, and uncertainties. This document contains a general discussion of various aspects of these equilibrium measurements as well as STRENDA (Standards for Reporting Enzymology Data) recommendations regarding the measurements and the reporting of results.

Excess Absorbance as a Novel Approach for Studying the Self-Aggregation of Vital Dyes in Liquid Solution.

In the present paper, a simple method for analyzing the self-aggregation of dyes in a solution by a UV-visible absorption measurements is proposed. The concept of excess absorbance is introduced to determine an equation whose coefficients determine the parameters of the aggregation equilibrium. The computational peculiarities of the model are first discussed theoretically and then applied to sodium fluorescein in polar protic and aprotic solvents, as well as in aqueous solutions of methylene blue, which is a cationic dye. Although the experimental responses are very different, the model appears to work equally well in both cases. The model reveals that the trimer is the most likely configuration in both solvents. Furthermore, aggregation is strongly favored for the protic solvent. Interestingly, the model establishes that in aqueous solutions of methylene blue, the tetramer is the predominant form, which has long been assumed and recently demonstrated with sophisticated computational techniques.

Conditional Equilibrium Constants Reviewed.

A free energy-based conceptual theoretical framework from which the conditional equilibrium constant can be comprehensibly understood is presented. This constant is found to be a weighted geometric mean of the equilibrium constants of the reactions of all forms of the conditioned species under buffering conditions, where the weight is given by a function of their predominance in terms of their mole fractions. Once it is shown that this type of equilibrium constant can be easily deduced form free energy functions, it is shown how corrections for activity coefficient can be incorporated as well. The framework additionally permits to interpret side-reactions coefficients as free energy terms related to the chemical speciation of the system, allowing the use of the generalization of Hess' law to obtain conditional constants and a straightforward deduction of multiconditional equilibrium constants. Furthermore, different uses of the conditional constants along the actual literature are reviewed as well allowing to have a complete and updated panorama of the employment of this important concept in chemical and speciation analysis in many areas of research.

The missing hydrogen ion, part-1: Historical precedents vs. fundamental concepts.

The purpose of this review and commentary was to provide an historical and evidence-based account of organic acids and the biochemical and organic chemistry evidence for why cells do not produce metabolites that are acids. The scientific study of acids has a long history dating to the 16th and 17th centuries, and the definition of an acid was proposed in 1884 as a molecule that when in an aqueous solution releases a hydrogen ion (H+). There are three common ionizable functional groups for molecules classified as acids: 1) the carboxyl group, 2) the phosphoryl group and 3) the amine group. The propensity by which a cation will associate or dissociate with a negatively charged atom is quantified by the equilibrium constant (Keq) of the dissociation constant (Kd) of the ionization (Keq â€‹= â€‹Kd), which for lactic acid (HLa) vs. lactate (La-) is expressed as: Keq=Kd=[H+][La-][HLa]= 4 677.351 4 (ionic strength â€‹= â€‹0.01 Mol⋅L-1, T â€‹= â€‹25 â€‹°C). The negative log10 of the dissociation pKd reveals the pH at which half of the molecules are ionized, which for HLa â€‹= â€‹3.67. Thus, knowing the pKd and the pH of the solution at question will reveal the extent of the ionization vs. acidification of molecules that are classified as acids.

Determination of association equilibrium constant from single molecule fluorescence localization microscopy.

Single molecule fluorescence localization microscopy provides molecular localization with a precision in the tens of nanometer range in the plane perpendicular to the light propagation. This opens the possibility to count molecules and correlate their locations, starting from a map of the actual positions in a single molecule super resolution image. Considering molecular pair correlation as an indication of interaction, and a way to discern them from free molecules, we describe a method to calculate thermodynamic equilibrium constants. In this work, we use as a test system two complementary homo-oligonucleotides, one strand marked with Cyanine 3.5 and the other with Alexa Fluor 647. Hybridization is controlled by the amount of each strand, temperature, and the ionic force, and measured in steady state emission. The same samples are examined in Stochastic Optical Reconstruction Microscopy (STORM) experiments with split-field simultaneous two-colour detection. The effect of multiblinking, labelling-detection efficiency, and determination of the critical distance for association are discussed. We consistently determine values in STORM coincident with those of the bulk experiment.

Discussion on the thermodynamic calculation by distribution constant in Journal of Contaminant Hydrology 243 (2021) 103906.

This comment discussed the calculation of thermodynamic parameters about the paper published in Journal of Contaminant Hydrology 243 (2021) 103906. Despite the paper's novelty and innovation, the distribution constant (Kd) with a dimension of L/mg is not the standard equilibrium constant (Ko), therefore, it cannot be used to calculate the thermodynamic parameters. By analyzing the incorrect results and providing the reasonable method for calculating the thermodynamic parameters，this comment is helpful to understand the calculation principle of thermodynamic parameters by the distribution constant and avoid the misuse of incorrect formulas.

Comments on the calculation of the standard equilibrium constant using the Langmuir model in Journal of Hazardous Materials 422 (2022) 126863.

The calculation of equilibrium constant from the Langmuir model is widely used in the literature. However, the dimensional problem of the equilibrium constant has often been ignored. For example, a recent publication on the strong properties of the new adsorbent for tetracycline. Nevertheless, this used an improper calculation of the standard equilibrium constant, confusing solute and solution. This creates dimension for K0 obtained from Eq. (13). Unfortunately, K0 should be dimensionless. In this comment, the origin and background of this kind of error is analyzed and the method for correcting the error is presented. Specifically, we establish a clear relationship between the Langmuir constant (KL) and the standard equilibrium constant (K0). We hope this comment clarifies the essence of calculating the standard equilibrium constant by using the Langmuir model, so others avoid the propagation of this kind of error.

Comment on the calculation of equilibrium constant and thermodynamic parameters by the distribution coefficient in Environmental Research 203 (2022) 111814.

This comment discussed the calculation of equilibrium constant and thermodynamic parameters in the paper of Kayalvizhi et al. (2022). This paper is of high academic value, however, there are some calculation and quotation errrors. The equilibrium constant K evolved from the distribution coefficient has a dimension of L/g, which is not the standard equilibrium constant, therefore, it cannot be used to calculate the thermodynamic parameters. This comment firstly analyzed the calculation errors made by Kayalvizhi et al. (2022), then established the relationship between distribution coefficient and standard equilibirum constant, and recalculated the thermodynamic parameters by using the correct distribution coefficient equation. As a research paper, authors not only provide the originality and novelty, but also give its correct results. This comment can bring to the attention of readers, authors, editors and reviewers about the thermodynamic calculation. At the same time, it is helpful to avoid the misuse and propagation of the incorrect equation in the area of adsorption thermodynamics.

Two Intercalation Mechanisms of Oxazole Yellow Dimer (YOYO-1) into DNA.

The oxazole yellow dye, YOYO-1 (a symmetric homodimer), is a commonly used molecule for staining DNA. We applied the brightness analysis to study the intercalation of YOYO-1 into the DNA. We distinguished two binding modes of the dye to dsDNA: mono-intercalation and bis-intercalation. Bis-intercalation consists of two consecutive mono-intercalation steps, characterised by two distinct equilibrium constants (with the average number of base pair per binding site equals 3.5): K1=3.36±0.43×107M-1 and K2=1.90±0.61×105M-1, respectively. Mono-intercalation dominates at high concentrations of YOYO-1. Bis-intercalation occurs at low concentrations.

Removal of phenolic compounds from de-oiled sunflower kernels by aqueous ethanol washing.

Selective removal of phenolic compounds (PCs) from de-oiled sunflower kernel is generally considered a key step for food applications, but this often leads to protein loss. PC removal yield and protein loss were assessed during an aqueous or aqueous ethanol washing process with different temperatures, pH-values and ethanol contents. PC yield and protein loss increased when the ethanol content was < 60% or when a higher temperature was applied. Our main finding is that preventing protein loss should be the key objective when selecting process conditions. This can be achieved using solvents with high ethanol content. Simulation of the multi-step exhaustive process showed that process optimization is possible with additional washing steps. PC yield of 95% can be achieved with only 1% protein loss using 9 steps and 80% ethanol content at 25℃. The functional properties of the resulting concentrates were hardly altered with the use of high ethanol solvents.

Determining the domain-level reaction-diffusion properties of an actin-binding protein transgelin-2 within cells.

Proteins in cells undergo repeated binding to other molecules, thereby reducing the apparent extent of their intracellular diffusion. While much effort has been made to analytically decouple these combined effects of pure diffusion and chemical binding, it is difficult with conventional approaches to attribute the measured quantities to the nature of specific domains of the proteins. Motivated by the common goal in cell signaling research aimed at identifying the domains responsible for particular intermolecular interactions, here we describe a framework for determining the local physicochemical properties of cellular proteins associated with immobile scaffolds. To validate this new approach, we apply it to transgelin-2, an actin-binding protein whose intracellular dynamics remains elusive. We develop a fluorescence recovery after photobleaching (FRAP)-based framework, in which comprehensive combinations of domain-deletion mutants are created, and the difference among them in FRAP response is analyzed. We demonstrate that transgelin-2 in actin stress fibers (SFs) interacts with F-actin via two separate domains, and the chemical properties are determined for the individual domains. Its pure diffusion properties independent of the association to F-actin is also obtained. Our approach will thus be useful, as presented here for transgelin-2, in addressing the signaling mechanism of cellular proteins associated with SFs.

Immunochemical method for penthiopyrad detection through thermodynamic and kinetic characterization of monoclonal antibodies.

Immunoassays are nowadays being employed for rapid contaminant analysis in clinical, environmental, and agrochemical samples. A thorough characterization of the antibody‒antigen interaction can bring light to the immunoreagent selection process in order to develop sensitive and robust tests. Thus, determination of equilibrium and reaction rate constants is usually recommendable. However, this can be quite tricky for low molecular weight compounds, and competitive strategies are commonly followed to estimate apparent affinity values. In the present study, a collection of monoclonal antibodies to penthiopyrad was raised for the first time, and apparent equilibrium constants were assessed by the Langmuir model using three different competitive enzyme-linked immunosorbent assay formats. The obtained KD values from antibody-coated assays were quite close to the corresponding KD values calculated from surface plasmon resonance (SPR) evaluation. These studies were employed to select a pair of immunoreagents for immunoassay development. The KD value for penthiopyrad of the selected antibody obtained by SPR was 0.28 nM. The optimized direct assay showed an IC50 value for penthiopyrad of 0.42 nM (0.15 ng mL-1) in buffer. The limit of quantification for grape, must, and wine samples was 10 ng mL-1. An excellent correlation was found when immunochemical results were compared with those from LC-MS/MS. As an application case, it was determined that 58% of penthiopyrad was still found in wine after fermentation.

Optimized Biocatalytic Synthesis of 2-Selenopyrimidine Nucleosides by Transglycosylation*.

Selenium-modified nucleosides are powerful tools to study the structure and function of nucleic acids and their protein interactions. The widespread application of 2-selenopyrimidine nucleosides is currently limited by low yields in established synthetic routes. Herein, we describe the optimization of the synthesis of 2-Se-uridine and 2-Se-thymidine derivatives by thermostable nucleoside phosphorylases in transglycosylation reactions using natural uridine or thymidine as sugar donors. Reactions were performed at 60 or 80 °C and at pH 9 under hypoxic conditions to improve the solubility and stability of the 2-Se-nucleobases in aqueous media. To optimize the conversion, the reaction equilibria in analytical transglycosylation reactions were studied. The equilibrium constants of phosphorolysis of the 2-Se-pyrimidines were between 5 and 10, and therefore differ by an order of magnitude from the equilibrium constants of any other known case. Hence, the thermodynamic properties of the target nucleosides are inherently unfavorable, and this complicates their synthesis significantly. A tenfold excess of sugar donor was needed to achieve 40-48 % conversion to the target nucleoside. Scale-up of the optimized conditions provided four Se-containing nucleosides in 6-40 % isolated yield, which compares favorably to established chemical routes.

Words of advice: teaching enzyme kinetics.

Enzymology is concerned with the study of enzyme structure, function, regulation and kinetics. It is an interdisciplinary subject that can be treated as an exclusive sphere of exhaustive inquiry within mathematical, physico-chemical and biological sciences. Hence, teaching of enzymology, in general, and enzyme kinetics, in particular, should be undertaken in an interdisciplinary manner for a holistic appreciation of this subject. Further, analogous examples from everyday life should form an integral component of the teaching for an intuitive grasp of the subject matter. Furthermore, simulation-based appreciation of enzyme kinetics should be preferred over simplifying assumptions and approximations of traditional enzyme kinetics teaching. In this Words of Advice, I outline the domain depth of enzymology across the various disciplines and provide initial ideas on how appropriate analogies can provide firm insights into the subject. Further, I demonstrate how an intuitive feel for the subject can help not only in grasping abstract concepts but also extending it in experimental design and subsequent interpretation. Use of simulations in grasping complex concepts is also advocated given the advantages this medium offers over traditional approaches involving images and molecular models. Furthermore, I discuss the merits of incorporating the historical backdrop of major discoveries in enzymological teaching. We, at AstraZeneca, have experimented with this approach with the desired outcome of generating interest in the subject from people practising diverse disciplines.