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.     

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.     

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.     

Probabilistic description of the system "ligand-receptor"

The theory of probabilities was used to describe the ligand-receptor interaction. Mean and variance of number ligand-receptor complexes are calculated. It is shown that the mean number of ligand-receptor complexes coincides with that obtained from the law of conservation masses. Proceeding from a ratio of mean and expectation it is shown that the variance of the number of ligand-receptor complexes should be taken into account with concentration of ligand-receptor complexes component less than 1 fmol.     

A Tunable Coarse-Grained Model for Ligand-Receptor Interaction

Cell-surface receptors are the most common target for therapeutic drugs. The design and optimization of next generation synthetic drugs require a detailed understanding of the interaction with their corresponding receptors. Mathematical approximations to study ligand-receptor systems based on reaction kinetics strongly simplify the spatial constraints of the interaction, while full atomistic ligand-receptor models do not allow for a statistical many-particle analysis, due to their high computational requirements. Here we present a generic coarse-grained model for ligand-receptor systems that accounts for the essential spatial characteristics of the interaction, while allowing statistical analysis. The model captures the main features of ligand-receptor kinetics, such as diffusion dependence of affinity and dissociation rates. Our model is used to characterize chimeric compounds, designed to take advantage of the receptor over-expression phenotype of certain diseases to selectively target unhealthy cells. Molecular dynamics simulations of chimeric ligands are used to study how selectivity can be optimized based on receptor abundance, ligand-receptor affinity and length of the linker between both ligand subunits. Overall, this coarse-grained model is a useful approximation in the study of systems with complex ligand-receptor interactions or spatial constraints.     

Dynamics of the Adair model for ligand-receptor binding

The dynamics of the Adair model for ligand-receptor binding involving the case with interacting receptors is investigated. Using the methods of formal reaction kinetics, the existence, uniqueness, and asymptotic stability of equilibria within the model are demonstrated. The approximate solutions to the Adair model are found.     

Multiple receptor states are required to describe both kinetic binding and activation of neutrophils via N-formyl peptide receptor ligands

It is well-established that the binding of N-formyl peptides to the N-formyl peptide receptor on neutrophils can be described by a kinetic scheme that involves two ligand-bound receptor states, both a low affinity ligand-receptor complex and a high affinity ligand-receptor complex, and that the rate constants describing ligand-receptor binding and receptor affinity state interconversion are ligand-specific. Here we examine whether differences due to these rate constants, i.e. differences in the numbers and lifetimes of particular receptor states, are correlated with neutrophil responses, namely actin polymerization and oxidant production. We find that an additional receptor state, one not discerned from kinetic binding assays, is required to account for these responses. This receptor state is interpreted as the number of low affinity bound receptors that are capable of activating G proteins; in other words, the accumulation of these active receptors correlates with the extent of both responses. Furthermore, this analysis allows for the quantification of a parameter that measures the relative strength of a ligand to bias the receptor into the active conformation. A model with this additional receptor state is sufficient to describe response data when two ligands (agonist/agonist or agonist/antagonist pairs) are added simultaneously, suggesting that cells respond to the accumulation of active receptors regardless of the identity of the ligand(s).     

Extending Bell's model: how force transducer stiffness alters measured unbinding forces and kinetics of molecular complexes

Forced unbinding of complementary macromolecules such as ligand-receptor complexes can reveal energetic and kinetic details governing physiological processes ranging from cellular adhesion to drug metabolism. Although molecular-level experiments have enabled sampling of individual ligand-receptor complex dissociation events, disparities in measured unbinding force F_R among these methods lead to marked variation in inferred binding energetics and kinetics at equilibrium. These discrepancies are documented for even the ubiquitous ligand-receptor pair, biotin-streptavidin. We investigated these disparities and examined atomic-level unbinding trajectories via steered molecular dynamics simulations, as well as via molecular force spectroscopy experiments on biotin-streptavidin. In addition to the well-known loading rate dependence of F_R predicted by Bell's model, we find that experimentally accessible parameters such as the effective stiffness of the force transducer k can significantly perturb the energy landscape and the apparent unbinding force of the complex for sufficiently stiff force transducers. Additionally, at least 20% variation in unbinding force can be attributed to minute differences in initial atomic positions among energetically and structurally comparable complexes. For force transducers typical of molecular force spectroscopy experiments and atomistic simulations, this energy barrier perturbation results in extrapolated energetic and kinetic parameters of the complex that depend strongly on k. We present a model that explicitly includes the effect of k on apparent unbinding force of the ligand-receptor complex, and demonstrate that this correction enables prediction of unbinding distances and dissociation rates that are decoupled from the stiffness of actual or simulated molecular linkers.     

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.     

Reevaluation of ANS binding to human and bovine serum albumins: key role of equilibrium microdialysis in ligand - receptor binding characterization

In this work we return to the problem of the determination of ligand-receptor binding stoichiometry and binding constants. In many cases the ligand is a fluorescent dye which has low fluorescence quantum yield in free state but forms highly fluorescent complex with target receptor. That is why many researchers use dye fluorescence for determination of its binding parameters with receptor, but they leave out of account that fluorescence intensity is proportional to the part of the light absorbed by the solution rather than to the concentration of bound dye. We showed how ligand-receptor binding parameters can be determined by spectrophotometry of the solutions prepared by equilibrium microdialysis. We determined the binding parameters of ANS - human serum albumin (HSA) and ANS - bovine serum albumin (BSA) interaction, absorption spectra, concentration and molar extinction coefficient, as well as fluorescence quantum yield of the bound dye. It was found that HSA and BSA have two binding modes with significantly different affinity to ANS. Correct determination of the binding parameters of ligand-receptor interaction is important for fundamental investigations and practical aspects of molecule medicine and pharmaceutics. The data obtained for albumins are important in connection with their role as drugs transporters.     

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.     

Analysis ligand-receptor interactions from the molecular to the organism levels

A system of quantitative analysis is proposed for evaluation of ligand-receptor interaction on models of different levels of complexity. For two discrete receptor pools, binding of radio-labelled ligands to specific receptors and the magnitude of physiological response for an effector system with two discrete pools of receptors with different affinities are described with the aid of developed respective equations. The equations' parameters characterise properties of the effector system under study: the number of receptor pools differing in their affinity to a ligand; the number of active receptors of the maximum response magnitude; and the number of ligand's molecules bound to the receptor. The derived parameter's efficiency provides a general characteristic of affinity for the effector system under study. The described method of analysis of the ligand-receptor interactions is applicable to studies of any biological responses yielding quantitative results.     

Stability of molecular adhesion mediated by confined polymer repellers and ligand-receptor bonds

Experiments have shown that stable adhesion of a variety of animal cells on substrates prepared with precisely controlled ligand distribution can be formed only if the ligand spacing is below 58 nm. To explain this phenomenon, here we propose a confined polymer model to study the stability of molecular adhesion mediated by polymer repellers and ligand-receptor bonds. In this model, both repellers and binders are treated as wormlike chains confined in a nanoslit, and the stability of adhesion is considered as a competition between attractive interactions of ligand-receptor binding and repulsive forces due to the size mismatch between repellers and binders. The force on each ligand-receptor bond is calculated from the confined polymer model, and the classic model of Bell is used to describe the association/dissociation reactions of ligand-receptor bonds. The calculated equilibrium bond distribution shows that there exists a critical ligand density for stable adhesion, corresponding to a critical ligand spacing which agrees not only qualitatively but also quantitatively with the experimental observation. In the case of stable adhesion, the model predicts an equilibrium separation between adhesion surfaces below 60% of the contour length of the ligand-receptor bonds.     

Solid supports in enzyme-linked immunosorbent assay and other solid-phase immunoassays

A very large proportion of modern immunoassays involve the use of synthetic solid phases to immobilize one of the reactants. These solid-phase immunoassays (SPIs) therefore involve ligand-receptor interactions that occur within a reaction volume close to the solution/solid phase interface. As a consequence, the immunochemistry/biochemistry of these ligand-receptor interactions differs from that of their counterparts in solution. Furthermore, the immobilization process can significantly alter the biological activity of the reactant; most adsorbed proteins on polystyrene or silicone are partially or largely denatured. Therefore the use of alternative methods of immobilization is attractive but may result in little increase in the amount of total functional reactant. However, all commonly used solid phases do not have the same properties or the same capacity for reactant immobilization or experience the same level of nonspecific binding. Empiricism plays a major role in SPIs. Derivations of mass law equations for measuring the antigen capture of solid-phase antibodies, for determining the affinity of solid phase for protein adsorption, and for estimating antibody affinity are reviewed.     

Ligand-receptor interaction. Klotz-Hunston problem for two classes of binding sites and its solution

The problem of the affinity and quantity determination of two classes of binding sites for ligand-receptor interaction using either Scatchard or Klotz plots was considered. Klotz and Hunston previously solved this problem only for the case of a representation of experimental data using the Scatchard plot. Since their publication, it was the common view that only the use of the Scatchard plot allows solving this problem. However, in some cases, using the Klotz plot is more convenient for a representation of experimental data concerning ligand-receptor interaction, though usually, this plot was used only for the evaluation of receptor affinity with one class of binding sites. In the present paper, it was demonstrated that Klotz plot also could be used for the evaluation affinity and quantity of two classes of binding sites.     

Stoichiometry of interaction between interferon gamma and its receptor.

The biological response of interferon gamma is mediated by binding to a specific cell-surface receptor. We investigated the stoichiometry of this binding using soluble receptors produced in prokaryotic and eukaryotic expression systems comprising the extracellular ligand-binding domain of the native protein. The ligand-receptor complexes were analyzed by cross-linking, chromatography, analytical ultracentrifugation and laser-light scattering. Cross-linking and chromatography showed that the stoichiometry of the interaction between ligand and receptor depends on the molar ratios of the two components mixed. All approaches confirmed that mixtures of ligand-receptor complexes are formed with one interferon-gamma dimer bound by one or two receptors. The soluble receptor produced in Escherichia coli mainly showed a ligand/receptor stoichiometry of 1:1, while the receptors produced in eukaryotic cells showed a stoichiometry of binding of 1:2. This apparent discrepancy is most likely due to the conformational heterogeneity of the Escherichia-coli-derived protein.     

Steric effects on multivalent ligand-receptor binding: exclusion of ligand sites by bound cell surface receptors.

Steric effects can influence the binding of a cell surface receptor to a multivalent ligand. To account for steric effects arising from the size of a receptor and from the spacing of binding sites on a ligand, we extend a standard mathematical model for ligand-receptor interactions by introducing a steric hindrance factor. This factor gives the fraction of unbound ligand sites that are accessible to receptors, and thus available for binding, as a function of ligand site occupancy. We derive expressions for the steric hindrance factor for various cases in which the receptor covers a compact region on the ligand surface and the ligand expresses sites that are distributed regularly or randomly in one or two dimensions. These expressions are relevant for ligands such as linear polymers, proteins, and viruses. We also present numerical algorithms that can be used to calculate steric hindrance factors for other cases. These theoretical results allow us to quantify the effects of steric hindrance on ligand-receptor kinetics and equilibria.