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.     

Consequences of ligand bivalency in interactions involving particulate receptors: equilibrium and kinetic studies with Sephadex-concanavalin A, butylagarose-phosphorylase b, and Fc receptor-IgG dimer interactions as model systems

Theoretical consideration is given to the interaction of a bivalent ligand with particulate receptor sites, not only from the viewpoint of quantitatively describing the binding behavior but also from that of the kinetics of ligand release upon infinite dilution of a receptor-ligand mixture. In the latter regard, a general expression is derived that describes the time dependence of the amount of ligand bound as a function of two rate constants for the stepwise dissociation of cross-linked ligand-receptor complex and a thermodynamic parameter expressing the initial ratio of singly linked to doubly linked ligand-receptor complexes. An experimental study of the interaction between Sephadex and concanavalin A is then used to illustrate application of this recommended theoretical approach for characterizing the binding behavior and dissociation kinetics of a bivalent ligand for a system in which all ligand-receptor interactions may be described by a single intrinsic association constant. Published results on the interaction of phosphorylase b with butylagarose are also shown to comply with this simplest model of the bivalent ligand hypothesis; but those for the interaction between immunoglobulin G (IgG) dimers and Fc receptors require modification of the model by incorporation of different intrinsic association constants for the successive binding of receptor sites to the bivalent ligand. These results emphasize the need to consider ligand bivalency as a potential phenomenon in studies of interactions between protein ligands and particulate receptors and illustrate procedures by which the effects of ligand bivalency may be identified and characterized.     

Modeling Multivalent Ligand-Receptor Interactions with Steric Constraints on Configurations of Cell-Surface Receptor Aggregates

We use flow cytometry to characterize equilibrium binding of a fluorophore-labeled trivalent model antigen to bivalent IgE-FcεRI complexes on RBL cells. We find that flow cytometric measurements are consistent with an equilibrium model for ligand-receptor binding in which binding sites are assumed to be equivalent and ligand-induced receptor aggregates are assumed to be acyclic. However, this model predicts extensive receptor aggregation at antigen concentrations that yield strong cellular secretory responses, which is inconsistent with the expectation that large receptor aggregates should inhibit such responses. To investigate possible explanations for this discrepancy, we evaluate four rule-based models for interaction of a trivalent ligand with a bivalent cell-surface receptor that relax simplifying assumptions of the equilibrium model. These models are simulated using a rule-based kinetic Monte Carlo approach to investigate the kinetics of ligand-induced receptor aggregation and to study how the kinetics and equilibria of ligand-receptor interaction are affected by steric constraints on receptor aggregate configurations and by the formation of cyclic receptor aggregates. The results suggest that formation of linear chains of cyclic receptor dimers may be important for generating secretory signals. Steric effects that limit receptor aggregation and transient formation of small receptor aggregates may also be important.     

Avidity of bivalent antibodies. Problems of its experimental determination and theoretical evaluation

Some problems of experimental determination or theoretical evaluation of antibody avidity are considered. It was shown that in order to determine the fraction of nonoccupied antibodies in their mixture with the excess of the corresponding antigen which is required to estimate avidity the methods should be used which are more sensitive than ELISA. The available methods did not allow determining the avidity of bivalent antibodies because of many reasons. However, in the recent years new methods were suggested that make it possible to evaluate the avidity of bivalent antibodies and that of the receptors which consist of two binding sites connected by a flexible linker of the known length. Thus, there are all possibilities now for determining the avidity of bivalent antibodies in experiments or by theoretical methods.     

Probing 2-dimensional protein-protein interactions on model membranes

This protocol describes an in vitro approach for measuring the kinetics and affinities of interactions between membrane-anchored proteins. This method is particularly established for dissecting the interaction dynamics of cytokines with their receptor subunits. For this purpose, the receptor subunits are tethered in an orientated manner onto solid-supported lipid bilayers by using multivalent chelator lipids. Interaction between the ligand with the receptor subunits was probed by a combination of surface-sensitive spectroscopic detection techniques. Label-free detection by reflectance interferometry is used for following assembly of the membrane and tethering of the receptor subunits in quantitative terms. Total internal reflection spectroscopy is used for monitoring ligand binding to the membrane-anchored receptor, for monitoring ligand-receptor interactions by FRET and for monitoring ligand-exchange kinetics. These assays can be used for determining the affinities and stabilities of ligand-receptor complexes in plane of the membrane. The techniques described in this protocol can be established in 2-3 months.     

Cell-specific targeting by heterobivalent ligands

Current cancer therapies exploit either differential metabolism or targeting to specific individual gene products that are overexpressed in aberrant cells. The work described herein proposes an alternative approach--to specifically target combinations of cell-surface receptors using heteromultivalent ligands ("receptor combination approach"). As a proof-of-concept that functionally unrelated receptors can be noncovalently cross-linked with high avidity and specificity, a series of heterobivalent ligands (htBVLs) were constructed from analogues of the melanocortin peptide ligand ([Nle(4), dPhe(7)]-α-MSH) and the cholecystokinin peptide ligand (CCK-8). Binding of these ligands to cells expressing the human Melanocortin-4 receptor and the Cholecystokinin-2 receptor was analyzed. The MSH(7) and CCK(6) were tethered with linkers of varying rigidity and length, constructed from natural and/or synthetic building blocks. Modeling data suggest that a linker length of 20-50 ? is needed to simultaneously bind these two different G-protein coupled receptors (GPCRs). These ligands exhibited up to 24-fold enhancement in binding affinity to cells that expressed both (bivalent binding), compared to cells with only one (monovalent binding) of the cognate receptors. The htBVLs had up to 50-fold higher affinity than that of a monomeric CCK ligand, i.e., Ac-CCK(6)-NH(2). Cell-surface targeting of these two cell types with labeled heteromultivalent ligand demonstrated high avidity and specificity, thereby validating the receptor combination approach. This ability to noncovalently cross-link heterologous receptors and target individual cells using a receptor combination approach opens up new possibilities for specific cell targeting in vivo for therapy or imaging.     

Linker Dependence of Avidity in Multivalent Interactions Between Disordered Proteins

Multidomain proteins often interact through several independent binding sites connected by disordered linkers. The architecture of such linkers affects avidity by modulating the effective concentration of intramolecular binding. The linker dependence of avidity has been estimated theoretically using simple physical models, but such models have not been tested experimentally because the effective concentrations could not be measured directly. We have developed a model system for bivalent protein interactions connected by disordered linkers, where the effective concentration can be measured using a competition experiment. We characterized the bivalent protein interactions kinetically and thermodynamically for a variety of linker lengths and interaction strengths. In total, this allowed us to critically assess the existing theoretical models of avidity in disordered, multivalent interactions. As expected, the onset of avidity occurs when the effective concentration reached the dissociation constant of the weakest interaction. Avidity decreased monotonously with linker length, but only by a third of what is predicted by theoretical models. We suggest that the length dependence of avidity is attenuated by compensating mechanisms such as linker interactions or entanglement. The direct role of linkers in avidity suggests they provide a generic mechanism for allosteric regulation of disordered, multivalent proteins.     

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.     

Steroidal bivalent ligands for the estrogen receptor: Design,synthesis, characterization and binding affinities

Steroidal bivalent ligands for the estrogen receptor (ER) were designed using crystal structures of ERα dimers as a template. The syntheses of several 17α-ethynylestradiol-based bivalent ligands with varying linker compositions and lengths are described. The binding affinities of these bivalent ligands for ERα and ERβ were determined. In the two series of bivalent ligands that we synthesized, there is a clear correlation between linker length and binding affinity, both of which reach a maximum at the same tether length. Further studies are underway to explore aspects of bivalent ligand and control compound binding to the ERs and their effects on ER dimer formation; these results will be reported in a subsequent publication.     

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.     

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.     

Design, synthesis and in vitro evaluation of novel bivalent S-adenosylmethionine analogues

In optimal cases, bivalent ligands can bind with exceptionally high affinity to their protein targets. However, designing optimised linkers, that orient the two binding groups perfectly, is challenging, and yet crucial in both fragment-based ligand design and in the discovery of bisubstrate enzyme inhibitors. To further our understanding of linker design, a series of novel bivalent S-adenosylmethionine (SAM) analogues were designed with the aim of interacting with the MetJ dimer in a bivalent sense (1:1 ligand/MetJ dimer). A range of ligands was synthesised and analyzed for ability to promote binding of the Escherichia coli methionine repressor, MetJ, to its operator DNA. Binding of bivalent SAM analogues to the MetJ homodimer in the presence of operator DNA was evaluated by fluorescence anisotropy and the effect of linker length and structure was investigated. The most effective bivalent ligand identified had a flexible linker, and promoted the DNA-protein interaction at 21-times lower concentration than the corresponding monovalent control compound.     

The capping of receptors for the epidermal growth factor and the participation of the cytoskeleton in this process in A-431 cells

Epidermal growth factor (EGF) receptor capping results from the interaction between the receptors and polyvalent ligands in A-431 cells examined in suspension at 22 degrees C. Colocalization of actin and spectrin with the ligand-receptor complexes during the redistribution was shown using double immunofluorescence. The obtained data show that the cortical microfilaments are involved in capping. EGF receptors become associated with the Triton-insoluble cytoskeleton as a consequence of ligand binding. EGF-receptor capping is not sensitive to the action of cytochalasin B. Capping in A-431 cells is discussed as a new model for studying the redistribution of the ligand-receptor complex.     

Ligand affinity of the 67-kD elastin/laminin binding protein is modulated by the protein''s lectin domain: visualization of elastin/laminin-receptor complexes with gold-tagged ligands

Video-enhanced microscopy was used to examine the interaction of elastin- or laminin-coated gold particles with elastin binding proteins on the surface of live cells. By visualizing the binding events in real time, it was possible to determine the specificity and avidity of ligand binding as well as to analyze the motion of the receptor-ligand complex in the plane of the plasma membrane. Although it was difficult to interpret the rates of binding and release rigorously because of the possibility for multiple interactions between particles and the cell surface, relative changes in binding have revealed important aspects of the regulation of affinity of ligand-receptor interaction in situ. Both elastin and laminin were found to compete for binding to the cell surface and lactose dramatically decreased the affinity of the receptor(s) for both elastin and laminin. These findings were supported by in vitro studies of the detergent-solubilized receptor. Further, immobilization of the ligand-receptor complexes through binding to the cytoskeleton dramatically decreased the ability of bound particles to leave the receptor. The changes in the kinetics of ligand-coated gold binding to living cells suggest that both laminin and elastin binding is inhibited by lactose and that attachment of receptor to the cytoskeleton increases its affinity for the ligand.     

Rapid protein-ligand docking using soft modes from molecular dynamics simulations to account for protein deformability: binding of FK506 to FKBP

Most current docking methods to identify possible ligands and putative binding sites on a receptor molecule assume a rigid receptor structure to allow virtual screening of large ligand databases. However, binding of a ligand can lead to changes in the receptor protein conformation that are sterically necessary to accommodate a bound ligand. An approach is presented that allows relaxation of the protein conformation in precalculated soft flexible degrees of freedom during ligand-receptor docking. For the immunosuppressant FK506-binding protein FKBP, the soft flexible modes are extracted as principal components of motion from a molecular dynamics simulation. A simple penalty function for deformations in the soft flexible mode is used to limit receptor protein deformations during docking that avoids a costly recalculation of the receptor energy by summing over all receptor atom pairs at each step. Rigid docking of the FK506 ligand binding to an unbound FKBP conformation failed to identify a geometry close to experiment as favorable binding site. In contrast, inclusion of the flexible soft modes during systematic docking runs selected a binding geometry close to experiment as lowest energy conformation. This has been achieved at a modest increase of computational cost compared to rigid docking. The approach could provide a computationally efficient way to approximately account for receptor flexibility during docking of large numbers of putative ligands and putative docking geometries.     

Interpretation of Scatchard plots for aggregating receptor systems.

Aggregation of cell surface receptors, with each other or with other membrane proteins, occurs in a variety of experimental systems. The list of systems where receptor aggregation appears to be important in understanding ligand binding and cellular responses is growing rapidly. In this paper we explore the interpretation of equilibrium binding data for aggregating receptor systems. The Scatchard plot is a widely used tool for analyzing equilibrium binding data. The shape of the Scatchard plot is often interpreted in terms of multiple noninteracting receptor populations. Such an analysis does not provide a framework for investigating the role of receptor aggregation and will be misleading if there is a relation between receptor aggregation and ligand binding. We present a general model for the equilibrium binding of a ligand with any number of aggregating receptor populations and derive theoretical expressions for observable Scatchard plot features. These can be used to test particular models and estimate model parameters. We develop particular models and apply the general results in the cases of six aggregating receptor systems where ligand binding and receptor aggregation are related: cross-linking of monovalent cell surface proteins by monoclonal antibodies, cross-linking of cell surface antibodies by bivalent ligand, antibody-induced co-cross-linking of cell surface antibodies and Fc gamma receptors, ligand-enhanced aggregation of identical epidermal growth factor receptors, aggregation of heterologous receptors for interleukin 2 to form a high-affinity receptor, and association of receptors, including those for interleukins 5 and 6, with nonbinding accessory proteins that influence receptor affinity or effector function.     

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).     

Determination of the stable conformation of GABA(A)-benzodiazepine receptor bivalent ligands by low temperature NMR and X-ray analysis

The stable conformations of GABA(A)-benzodiazepine receptor bivalent ligands 2 and 3 were determined by low temperature NMR spectroscopy and confirmed by single crystal X-ray analysis. The linear conformation was important for these dimers to access the binding site and exhibit potent in vitro affinity as illustrated for alpha5 subtype selective ligand 2 (15 nM). Bivalent ligand 3 with the 5 atom linker folded back upon itself both in solution and in the solid state, moreover, it did not bind to Bz receptors.     

Quantitative relation between intermolecular and intramolecular binding of pro-rich peptides to SH3 domains

Flexible linkers are often found to tether binding sequence motifs or connect protein domains. Here we analyze three usages of flexible linkers: 1), intramolecular binding of proline-rich peptides (PRPs) to SH3 domains for kinase regulation; 2), intramolecular binding of PRP for increasing the folding stability of SH3 domains; and 3), covalent linking of PRPs and other ligands for high-affinity bivalent binding. The basis of these analyses is a quantitative relation between intermolecular and intramolecular binding constants. This relation has the form K(i) = K(e0)p for intramolecular binding and K(e) = K(e01)K(e02)p for bivalent binding. The effective concentration p depends on the length of the linker and the distance between the linker attachment points in the bound state. Several applications illustrate the usefulness of the quantitative relation. These include intramolecular binding to the Itk SH3 domain by an internal PRP and to a circular permutant of the alpha-spectrin SH3 domain by a designed PRP, and bivalent binding to the two SH3 domains of Grb2 by two linked PRPs. These and other examples suggest that flexible linkers and sequence motifs tethered to them, like folded protein domains, are also subject to tight control during evolution.     

Dissociation kinetics of bivalent ligand-immunoglobulin E aggregates in solution

We study the dissociation of preformed bivalent ligand-bivalent receptor aggregates in solution, where the ligand is a symmetric bivalent hapten with two identical 2,4-dinitrophenyl (DNP) groups and the receptor is a fluorescein-labeled monoclonal anti-DNP IgE. We promote dissociation in two ways: by the addition of high concentrations of a monovalent hapten that competes for IgE binding sites with the bivalent hapten and by the addition of high concentrations of unlabeled IgE that binds almost all ligand binding sites that dissociate from labeled IgE. We investigate both theoretically and experimentally the two types of dissociation and find them to be quite different. Theory predicts that their kinetics will depend differently on the fundamental rate constants that characterize binding and aggregation. Using monovalent ligand to promote dissociation, we find that the fraction of labeled IgE sites bound to bivalent ligand decays with a slow and fast component. The fast decay corresponds to the dissociation of a singly bound DNP hapten. The interpretation of the slow decay depends on the detailed way in which ligand-receptor aggregates break up. We show that one possible explanation of these data is that small stable rings form before the addition of monovalent ligand. Other possible explanations are also presented.