New capabilities in determining the binding parameters for ligand-receptor interaction

A new method for determining the binding parameters of ligand-receptor interaction is suggested. The method is based on the application of the so-called coordinate of dilution, suggested by us earlier. We demonstrated that it is possible to determine the binding characteristics of ligand-receptor interaction using either the measurement of the concentration of the ligand-receptor complex at a state of equilibrium or the concentration of free receptors at different dilutions of the studying ligand-receptor mixture. The method also allows the determination of the concentration of the ligand in a pre-existing ligand-receptor mixture without preliminary separation of the interacting counterparts. For this reason the suggested method could be especially useful when the studying very labile receptors for which purification from the corresponding ligand is very difficult or impossible.     

A simple and convenient approach for evaluation of the parameters of ligand-receptor interaction. Receptor blocking index and its application

A new approach for determination of the parameters for ligand-receptor interaction, which is based on so-called dilution coordinates, was developed earlier. Equations that allow evaluation of not only the affinity of ligand-receptor interaction but also of the amount of free (or occupied by corresponding ligand) receptors were suggested. The most important advantage of this approach as compared with well-known methods is the ability to determine the binding parameters for ligand-receptor interaction even for the cases in which ligand and receptor are already present in a mixture and separation of counterparts from each other is technically difficult or even impossible. Due to this reason, the proposed approach can be especially useful for studying interactions between highly-labile biological receptors and corresponding ligands as found in vivo. In the present paper I continue to consider how to determine the binding parameters for a given ligand-receptor interaction if the value of receptor blocking index is determined experimentally.     

New approach in evaluating affinity of bivalent antibodies by the method of surface plasmon resonance. Theory

Theoretical aspects of the affinity evaluation for the interaction between bivalent receptors (or antibodies) and corresponding ligands (or antigens) are considered. It was shown that the ligand presence in the solution at the stage when the receptor dissociation occurs leads to the increase of the affinity evaluation accuracy. We demonstrated that the analysis of the dissociative curve of the receptor from the chip is not necessary for affinity determination; the analysis of associative curve is sufficient for this purpose. We also suggested a new approach for evaluating the affinity of bivalent receptors (or antibodies) when these reagents are present in the studied solution and the correspondent ligand (or antigen) is immobilized on the chip.     

A new method for the evaluation of antibody affinity based on serial dilutions of studied antibody-antigen mixture

A new method for the evaluation of the affinity of bivalent antibodies were suggested. This method is based on the previously published by the author the idea of using so-called coordinates of dilutions. It was shown that the suggested method allows to evaluate the affinity of antibodies with high accuracy using this simple approach. It is supposed that at some conditions the suggested method could have substantial advantages in comparison to the traditional methods. This method allows to analyze situations when antibodies are already in a mixture with antigen, for example in the bloodstream in the case of infections or autoimmune diseases. The method provides useful approach for the evaluation not only antibody affinity, but also the concentration of circulated antigen.     

Determining the parameters for receptor-ligand interaction by serial dilution method for the case when the ligand and receptor are in a pre-existing mixture

New methods of determining the binding parameters for ligand-receptor interaction are considered. The considered approaches are based on the earlier suggested method of serial dilution and application of so-called coordinates of dilution. It was shown that the suggested methods allow to evaluate affinity constant and ligand concentration even for the case, when the receptor and corresponding ligand of unknown concentration are in a mixture and their separation from each other is impossible. In this connection the suggested methods are especially useful for studying the ligand-receptor interaction if the receptor is very liable and its purification from the ligand would cause drastic changes of its binding properties.     

The problem of prozone in serum antibody titration and its mathematical interpretation

The question of the mechanism of "prozone" creation was considered from the point of view of the concentrations of free and semi-blocked bivalent antibodies in the mixture of these antibodies with monovalent antigen. Using the so called "coordinates of dilution", suggested by the author earlier, it was possible to calculate the relationships between the concentrations of either free or semi-blocked bivalent antibodies and the dilution of the antigen-antibody mixture. It was shown that dilution of antigen-antibody mixture leads to an increase of the concentration of free bivalent antibodies and simultaneous sharp decrease of the concentration of semi-blocked antibodies. It is suggested, that such a relationship is quite enough for the creation of prozone effect in reactions, when only bivalent antibodies are active and semi-blocked antibodies compete with free antibodies, providing inhibition of the reaction.     

Heparan sulfate proteoglycan binding promotes APRIL-induced tumor cell proliferation

APRIL, a proliferation-inducing ligand, is a member of the tumor necrosis factor (TNF) family that is expressed by various types of tumors and influences their growth in vitro and in vivo. Two receptors, transmembrane activator and cyclophilin ligand interactor (TACI) and B-cell maturation antigen (BCMA), bind APRIL, but neither is essential for the tumor-promoting effects, suggesting that a third receptor exists. Here, we report that APRIL specifically binds to heparan sulfate proteoglycans (HSPG) on the surface of tumor cells. This binding is mediated by the heparin sulfate side chains and can be inhibited by heparin. Importantly, BCMA and HSPG do not compete, but can bind APRIL simultaneously, suggesting that different regions in APRIL are critical for either interaction. In agreement, mutation of three lysines in a putative heparin sulfate-binding motif, which is not part of the TNF fold, destroys interaction with HSPG, while binding to BCMA is unaffected. Finally, whereas interaction of APRIL with HSPG does not influence APRIL-induced proliferation of T cells, it is crucial for its tumor growth-promoting activities. We therefore conclude that either HSPG serve as a receptor for APRIL or that HSPG binding allows APRIL to interact with a receptor that promotes tumor growth.     

Ligand-receptor interactions: a new method for determining the binding parameters

A new experimental procedure and new plot coordinates that allow determination of the binding parameters of ligand-acceptor interaction have been proposed. Instead of titration of a constant concentration of receptors with changing concentrations of ligand, as requested by the well-known methods of Klotz and Scatchard, a series of sequential dilutions of the reacting ligand-receptor mixture is suggested. This allows the application of a new coordinate system that transforms the binding isotherms into straight lines. The case of one acceptor with two classes of receptors with different binding constants is also considered briefly, where the correspondent graphs are nonlinear. It is suggested that in some cases this approach can be a simple and convenient substitute of the broadly used methods of Klotz and Scatchard.     

Determination of the concentration of ligand-specific molecules, found in mixtures with ligand-nonspecific molecules

A new method, which allows determination of the concentration of ligand-specific molecules in a mixture of these molecules with biochemically similar but ligand-unspecific molecules, is suggested. The method is based on a partial exhaustion of the mixture on a column with immobilized ligand and determination of the part of ligand-specific molecules presented in exhausted mixture. The concentration of monoclonal antibodies specific to bovine serum albumin in a commercial "Sigma" preparation and concentration of polyreactive immunoglobulins in a commercial "Sigma" preparation of bovine immunoglobulins were determined by suggested method.     

Analysis of dose-dependent antibody titration curves

Several types of dose-response titration curves were considered. It was demonstrated that the use of the so-called coordinates of dilution suggested earlier by us allows one to analyze the titration curves, obtained either by ELISA, or by agglutination. Theoretical curves, obtained by the developed theory are very similar to those obtained in experiments. It was shown, that the analysis of the titration curves could give important information concerning antibody-blocking factors in titration sera or other samples of studied antibodies.     

New systems of coordinates in the study of ligand-receptor interaction

Two new coordinate systems that allow to determine the parameters of ligand-receptor interaction are suggested. These coordinate systems principally differ from the well-known coordinates of Klotz and Scatchard. It was shown that suggested coordinates were simpler and more convenient then coordinates of Klotz and Scatchard and in some cases was more informative. The case when a ligand interacts with two classes of non-identical independent receptors was also considered.     

Towards molecularly imprinted polymers selective to peptides and proteins. The epitope approach

In this paper, we describe the epitope approach to molecular imprinting. The applicability of molecular imprinting, a method that allows the preparation of biomimetic compounds (artificial receptors and antibodies), is extended by this approach. Our approach makes it possible to obtain imprinted polymers selective to peptides and proteins whereas, to date, molecular imprinting has been used primarily for the preparation of polymers that selectively bind to relatively low molecular weight substances. The epitope approach is based on using (as a template) a short peptide that represents only part of a larger peptide or protein (as an epitope represents an antigen), which in turn can be recognized by the synthesized polymer. It is demonstrated that although other parts of peptides can influence the process of molecular recognition, the polymers imprinted with a short peptide efficiently recognize both the template and larger peptides (for example, oxytocin) that possess the same C-terminal part of the structure.     

Comparison of the effects of chemical and isotopic dilution on the dissociation of bound labeled ligands

The dissociation of a labeled ligand from a binding structure to which it is reversibly attached can be promoted either by dilution or by chase. The kinetics of the dissociation brought up by dilution can be modified or not by the presence of various concentrations of cold ligand, according to the molecular mechanism of interaction. Analog computer simulation leads to the following results: (i) no cooperativity, monomolecular dissociation: no modification; (ii) positive or negative cooperativity (sequential models): acceleration, no modification, or slowing down (according to the kinetic constants); (iii) positive cooperativity (concerted model): no modification; (iv) two-step interaction: no modification if both interaction steps take place in the same phase, otherwise acceleration; and, (v) bimolecular association and dissociation: acceleration. This methodology could be used in order to characterize the molecular properties of various binding structures in the field of drug and hormone receptors as well as in enzymology.     

Analysis of some "insoluble" problems of determining the binding parameters of ligand-receptor interaction and methods of their solving

Some problems of the estimation of the parameters of ligand-receptor interaction (affinity, rate constants, valency, etc.) were considered. It was demonstrated that not only the Scatchard plot but also Klotz plot could be used for determining the parameters of ligand-receptor interaction for two types of binding sites of different affinity. A new approach and new coordinate systems for the estimation of the parameters of ligand-receptor interaction were suggested. It was shown that for the estimation of the affinity of putative monovalent antibodies by ELISA various equations, which are more precise and convenient than the Friguet et al. equations, could be obtained by the transformation of mass action law equation. The problem solution for the estimation by ELISA the affinity of two types of bivalent antibodies with different affinity and their concentrations for the case of the mixture of these antibodies was also suggested. The application of the proposed coordinate of dilution allows to solve the problem of determination of the parameters of ligand-receptor interaction (including antigen-antibody system) for the pre-existing ligand-receptor mixture without their preliminary separation and purification. This approach is especially important for the cases when the receptor is not stable enough to be isolated in the intact form from this mixture. It was shown that the well-known phenomenon of the prozone often observed under the titration of serum antibodies by the method of agglutination may get a mathematical explanation. Analytical solution of the problem of determining the velocity constant and the amount of the end product of the first order irreversible and reversible reaction kinetics was suggested, despite the fact that the process is described by the system of irrational equations. Mehods of asymptotic solution of transcendental irrational equations which describe the dynamics of reactions which mechanisms are subject to the so-called heterogeneous, successive, or competitive models have been considered. These methods permit the finding of the reaction rate constants and the amount of the end product, if the kinetics of the transformation of either initial, or end product of the reaction is known.     

Determination of the affinity of high- and low-affinity antibodies, which are in a mixture, using ELISA and the method of non-linear regression

It was shown that application of the method of non-linear regression for the solution of the equation, which relates the fraction of free antibodies in a mixture and antigen concentrations, allows to determine the affinity constants for two antibodies in a mixture. Such method is easier and more accurate than the suggested by us earlier method, which use the numerical solution of the appropriate four equations, that describe the relations between the experimental data obtained by ELISA, competing antigen concentration, and values of antibody affinity. In addition, the proposed method allows using much less quantity of experimental measurements without diminishing of the accuracy for the affinity constants evaluations.     

The major histocompatibility complex-restricted antigen receptor on T cells. IX. Role of accessory molecules in recognition of antigen plus isolated IA

Antibody inhibition studies were done to determine which molecules on the surface of the T cell hybridomas other than their receptors for antigen plus IAd were involved in interaction with antigen-presenting B cells, with artificial IAd membranes on glass beads, or with anti-receptor antibodies coupled to Sepharose beads. We found that T cell LFA-1 was only involved when B cells were used to present antigen plus IAd, whereas T cell L3T4 was involved in the response of T cells to antigen plus IAd either on cells or in artificial membranes, but not if anti-receptor antibodies were used to stimulate the T cells. From these results we concluded that LFA-1 may be involved in the recognition of a ligand on cells that was not present in artificial membranes, but that L3T4 might interact with a nonpolymorphic portion of class II molecules present in both intact antigen-presenting cells and the antigen-presenting artificial membranes.     

Advantages of two- or polyvalent binding of a receptor to the corresponding ligand in comparison to univalent binding

The features of monovalent and bivalent binding of receptors (or antibodies) with a polyvalent ligand (or with an antigen) are considered. It is shown that the rigid connection of the binding sites of the receptor brings to high increase of binding affinity for the corresponding ligand, but only in case if its epitopes are fully complementary to both sites of the receptor binding. If not, then there is no advantage of the binding of bivalent receptor before univalent binding. If the binding sites of the receptor are connected by a flexible linker, then regardless of location of epitopes of the corresponding ligand there is the successful fastening of receptor and ligand. Exactly the connection by a flexible linker is used by Nature in most cases at constructing of polyvalent receptors.     

VLR Recognition of TLR5 Expands the Molecular Characterization of Protein Antigen Binding by Non-Ig-based Antibodies

Variable lymphocyte receptors (VLRs) are unconventional adaptive immune receptors relatively recently discovered in the phylogenetically ancient jawless vertebrates, lamprey and hagfish. VLRs bind antigens using a leucine-rich repeat fold and are the only known adaptive immune receptors that do not utilize an immunoglobulin fold for antigen recognition. While immunoglobulin antibodies have been studied extensively, there are comparatively few studies on antigen recognition by VLRs, particularly for protein antigens. Here we report isolation, functional and structural characterization of three VLRs that bind the protein toll-like receptor 5 (TLR5) from zebrafish. Two of the VLRs block binding of TLR5 to its cognate ligand flagellin in functional assays using reporter cells. Co-crystal structures revealed that these VLRs bind to two different epitopes on TLR5, both of which include regions involved in flagellin binding. Our work here demonstrates that the lamprey adaptive immune system can be used to generate high-affinity VLR clones that recognize different epitopes and differentially impact natural ligand binding to a protein antigen.     

Analysis of ligand-binding data without knowledge of bound or free ligand molar concentration

A method is proposed to set the parameters in a nonlinear regression procedure to determine the equilibrium dissociation constant (Kd) and the high affinity receptor concentration (Bmax) of systems consisting of one ligand, one high affinity receptor, and n low affinity binding sites. This method is suitable when neither bound or free ligand formal concentrations nor the maximum of the binding signal can be deduced from the experimental data. The method makes use of (i) the abscissa of the first inflection point of the plot of any signal proportional to the binding of ligand to receptors versus the logarithm of the total ligand concentration, and (ii) the initial slope of the saturation curve plotted in direct coordinates. We first demonstrate that when such an inflection point exists, its abscissa lies between Bmax/2 + Kd(1 + d) and Bmax + 2Kd(1 + d), where d is a parameter representative of the binding to the low affinity sites. Second, we demonstrate that the initial slopes of two saturation curves in direct coordinates, where Bmax varies by a known factor, allows an estimation of the Bmax/Kd ratio, within certain limits. From these two sets of data it is subsequently possible to define a precise window for the values of both Bmax and Kd. The performance of the method has been evaluated in representative cases using Monte Carlo studies. The results establish conditions for the existence of an inflection point as well as the influence of low affinity binding, whether or not proportional to Bmax.     

Artificial in vivo antigen presentation by the APCs and subsequent T-cell activation: a feasibility analysis

Inappropriate antigen presentation by the antigen-presenting cells (APCs) is a cause of various diseases. One of the ways to combat these diseases is to immobilize the APCs near the infected tissue or a tissue which is susceptible to an antigen. The antigen is presented by the APCs present in the immobilized form on an implant and these upon binding to T(H)-cells result in triggering of a cascade of events as part of the natural immune response leading to the destruction of the antigen. This system has been modeled as a dialysis bag containing immobilized receptors inside the bag and the ligand diffusing out of the bag. The simulations show that by using the implant, the concentration of the ligand that has diffused into the tissue matrix can be substantially reduced and by suitably choosing the coupler size, the T(H)-cells can also effectively be activated.