Quantitative considerations of the consequences of an interplay between ligand binding and reversible adsorption of a macromolecular solute

Explicit expressions are derived which determine the equilibrium composition of mixtures comprising a multivalent, insoluble matrix, a multivalent, macromolecular solute (acceptor) and a univalent ligand. With three-reactant mixtures of this type a range of combinations of interactions is possible wherein the ligand interacts with either the acceptor or the matrix, in either event perturbing the acceptor-matrix equilibria. Theory encompassing this range of possibilities is written in terms of a single site-binding constant for each type of interaction to account, in general terms, for both multiple binding and crosslinking effects. These explicit thermodynamic relationships are discussed, with the use of reported findings on several biological systems, in two frameworks. First, it is established that the theory is applicable to the quantitative interpretation of affinity chromatography experiments designed to elucidate the thermodynamic interaction parameters governing the various types of interacting system. Second, it is emphasized that the relationships are also relevant to metabolite-induced changes in the subcellular distribution of macromolecular species.     

Studies of macromolecular heterogeneous associations involving cross-linking: a re-examination of the ovalbumin-lysozyme system

A system is considered in which a multivalent acceptor interacts with a bivalent ligand in solution to form an array of complexes via multiple binding and cross-linking reactions. With the use of reacted site probability functions expressions are derived in terms of a site binding constant which are of potential use in the interpretation of sedimentation equilibrium and binding results obtained with such systems. Their potential use is explored in relation to results obtained on the interacting ovalbumin-lysozyme system at pH 6.80, ionic strength 0.02. A comparison is made of this interpretation with that based on an interaction pattern involving only multiple binding of ligand in the absence of cross-linking effects. While both interpretations quantitatively describe certain results, it is shown, by invoking further experimental observations on apparent weight-average molecular weight and precipitation behavior, that the more favored interpretation is that involving the operation of a spectrum of forces leading to a large array of ovalbumin-lysozyme complexes, including those of the cross-linked type. It is stressed that the particular ovalbumin-lysozyme system is but one example of interaction between oppositely charged macromolecules and therefore that the derived equations may find wider application to such systems and those known to involve more specific cross-linking interactions.     

Fluorescence correlation spectroscopy and photobleaching recovery of multiple binding reactions. I. Theory and FCS measurements

Fluorescence correlation spectroscopy (FCS) and fluorescence photobleaching recovery (FPR) are two methods that may be used to measure diffusion and chemical reaction kinetics in small, labile systems such as biological cells. These methods are here applied to systems in which a fluorescent ligand can bind to a polyvalent substrate molecule in a multistep reaction sequence. The analytical theory for both FCS and FPR is extended to allow analysis of these kinds of systems. Experimental measurements of the binding of ethidium bromide to DNA by FCS confirm the theoretical analysis. (FPR measurements on the same system are reported in the accompanying paper.) The analysis shows that FCS and FPR perceive multivalent binding reactions differently. This difference results from the selective effect of the photobleaching process in the chemical reaction system. The development and results we report could have useful applications to a wide range of biopolymeric binding and assembly process.     

Aggregation of IgE-receptor complexes on rat basophilic leukemia cells does not change the intrinsic affinity but can alter the kinetics of the ligand-IgE interaction.

The aggregation of IgE anchored to high-affinity Fc epsilon receptors on rat basophilic leukemia (RBL) cells by multivalent antigens initiates transmembrane signaling and ultimately cellular degranulation. Previous studies have shown that the rate of dissociation of bivalent and multivalent DNP ligands from RBL cells sensitized with anti-DNP IgE decreases with increasing ligand incubation times. One mechanism proposed for this effect is that when IgE molecules are aggregated, a conformational change occurs that results in an increase in the intrinsic affinity of IgE for antigen. This possibility was tested by measuring the equilibrium constant for the binding of monovalent DNP-lysine to anti-DNP IgE under two conditions, where the cell-bound IgE is dispersed and where it has been aggregated into visible patches on the cell surface using anti-IgE and a secondary antibody. No difference in the equilibrium constant in these two cases was observed. We also measured the rate of dissociation of a monovalent ligand from cell surface IgE under these two conditions. Whereas the affinity for monovalent ligand is not altered by IgE aggregation, we observe that the rate of ligand dissociation from IgE in clusters is slower than the rate of ligand dissociation from unaggregated IgE. These results are discussed in terms of recent theoretical developments concerning effects of receptor density on ligand binding to cell surfaces.     

Graphical analysis of binding data reflecting competition between two ligands for the same acceptor sites

A theoretical expression is derived for the analysis of results from competitive binding studies in which two multivalent ligands compete for acceptor sites, and a linear transform is suggested for simple graphical representation and assessment of experimental results. The protocol is illustrated by application to competitive binding data, obtained by ultrafiltration, on the interactions of bovine serum albumin with two structurally similar organic anions, methyl orange and methyl red. In a second experimental study the present approach is then used to establish that lactate dehydrogenase and aldolase compete for the same myofibrillar sites of bovine cardiac muscle. Finally, numerically simulated behavior of systems with additional binding sites for either ligand is used to emphasize that the criterion for classical (complete) competition is agreement between an experimentally determined equilibrium constant for ligand binding and the apparent value deduced from competitive binding studies. Nevertheless, the present analysis of competitive binding data should still offer considerable scope for screening quantitatively the cross-reactivities of drug and antigen analogs for their respective specific protein-acceptor sites.     

Effects of heterogeneity and cooperativity on the forms of binding curves for multivalent ligands

An exploratory investigation is made of the binding behavior that is likely to be encountered with multivalent ligands under circumstances where a single intrinsic binding constant does not suffice to describe all acceptor-ligand interactions. Numerical simulations of theoretical binding behavior have established that current criteria for recognizing heterogeneity and cooperativity of acceptor sites on the basis of the deviation of the binding curve from rectangular hyperbolic form for univalent ligands also apply to the interpretation of the corresponding binding curves for multivalent ligands. However, for systems in which the source of the departure from equivalence and independence of binding sites resides in the ligand, these criteria are reversed. On the basis of these observations a case is then made for attributing results of an experimental binding study of the interaction between pyruvate kinase and muscle myofibrils to positive cooperativity of enzyme sites rather than to heterogeneity or negative cooperativity of the myofibrillar sites.     

Ligand effects on protein thermodynamic stability

A simple, partition-function formalism is used to describe the coupling between ligand binding and protein equilibrium unfolding. This general theoretical framework is shown to provide an adequate basis for the analysis of experimental ligand effects on the unfolding of complex protein systems. Nevertheless, the most important consequences of ligand binding for protein thermodynamic stability, as exposed by the partition-function approach, are found to be those demonstrated by Julian Sturtevant about 20 years ago.     

Biospecific adsorption of lysozyme onto monoclonal antibody ligand immobilized on nonporous silica particles

It is very important to understand the equilibrium and dynamic characteristics of biospecific adsorption (affinity chromatography) for both scientific and application purposes. Experimental equilibrium and dynamic column data are presented on the adsorption of lysozyme onto antibody immobilized on nonporous silica particles. The Langmuir model is found to represent the equilibrium experimental data satisfactorily, and the equilibrium association constants and heats of adsorption have been estimated for two systems with different ligand densities. The effects of nonspecific interactions are more pronounced in the system with low-density ligand. The dynamic interaction kinetic parameters are estimated by matching the predictions of a fixed-bed model with the experimental breakthrough curves. The agreement between theory and experiment is good for the initial phases of breakthrough, where the mechanism of biospecific adsorption is dominant. In the later phase (saturation neighborhood) of breakthrough, the effects of nonspecific interactions appear to be greater in the low-density ligand system. The kinetics of the nonspecific interactions were estimated from the data of the later phase of breakthrough and were found to be considerably slower than those attributed to biospecific adsorption.     

Reconciliation of classical and reacted‐site probability approaches to allowance for ligand multivalence in binding studies

The objective of this investigation is to engender greater confidence in the validity of binding equations derived for multivalent ligands on the basis of reacted‐site probability theory. To that end, a demonstration of the theoretical interconnection between expressions derived by the classical stepwise equilibria and reacted‐site probability approaches for univalent ligands is followed by the use of the traditional stepwise procedure to derive binding equations for bivalent and trivalent ligands. As well as demonstrating the unwieldy nature of the classical binding equation for multivalent ligand systems, that exercise has allowed numerical simulation to be used to illustrate the equivalence of binding curves generated by the two approaches. The advantages of employing a redefined binding function for multivalent ligands are also confirmed by subjecting the simulated results to a published analytical procedure that has long been overlooked. Copyright © 2013 John Wiley & Sons, Ltd.     

Database of protein complexes with multivalent binding ability: Bival‐bind

Phenomena of multivalent binding of ligands with receptors are ubiquitous in biology and of growing interest in material sciences. Multivalency can enhance binding affinity dramatically. To understand the mechanism of multivalent binding in more detail model systems of bi‐ and multivalent receptors are needed, but are difficult to find. Furthermore it is useful to know about multivalent receptors, which can serve as targets to design multivalent drugs. The present contribution tries to close this gap. The Bival‐Bind database ( http://agknapp.chemie.fu‐berlin.de/bivalbind ) provides a relatively complete list – 2073 protein complexes with less than 90% sequence identity – out of the protein database, which can serve as bi‐ or multivalent receptors. Steric clashes of molecular spacers – necessary to connect the monomeric ligand units – with the receptor surface can diminish binding affinity dramatically and, thus, abolish the expected enhancement of binding affinity due to the multivalency. The potential multivalent receptors in the Bival‐Bind database are characterized with respect to the receptor surface topography. A height profile between the receptor binding pockets is provided, which is an important information to estimate the influence of unfavorable spacer receptor interaction. Proteins 2014; 82:744–751. © 2013 Wiley Periodicals, Inc.     

Elucidation of direct competition and allosteric modulation of small‐molecular‐weight protein ligands using surface plasmon resonance methods

The present work introduces a surface plasmon resonance‐based method for the discrimination of direct competition and allosteric effects that occur in ternary systems comprising a receptor protein and two small‐molecular‐weight ligands that bind to it. Fatty acid binding protein 4, fructose‐1,6‐bisphosphatase and human serum albumin were used as model receptor molecules to demonstrate the performance of the method. For each of the receptor molecules, pairs of ligand molecules were selected for which either direct competition or an allosteric effect had already been determined by other methods. The method of discrimination introduced here is based on the surface plasmon resonance responses observed at equilibrium when an immobilized receptor protein is brought into contact with binary mixtures of interacting ligands. These experimentally determined responses are compared with the responses calculated using a theoretical model that considers both direct competition and allosteric ligand interaction modes. This study demonstrates that the allosteric ternary complex model, which enables calculation of the fractional occupancy of the protein by each ligand in such ternary systems, is well suited for the theoretical calculation of these types of responses. For all of the ternary systems considered in this work, the experimental and calculated responses in the chosen concentration ratio range were identical within a five‐σ confidence interval when the calculations considered the correct interaction mode of the ligands (direct competition or different types of allosteric regulation), and in case of allosteric modulation, also the correct strength of this effect. This study also demonstrates that the allosteric ternary complex model‐based calculations are well suited to predict the ideal concentration ratio range or even single concentration ratios that can serve as hot spots for discrimination, and such hot spots can drastically reduce the numbers of measurements needed for discrimination between direct competition and distinct modulation modes (neutral, positive or negative allostery). Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

On the influence of polyvalent ligands on membrane curvature

The suggestion is made that a polyvalent ligand attached to a membrane will induce a curvature in that membrane which is concave toward the side to which that ligand is bound. This article presents a semiquantitative thermodynamic analysis predicting this effect for a simple system. The criterion for equilibrium of the ligand membrane complex is stated and for the simple system this is calculated for an arbitrary set of parameters. The influence of changes in these parameters is discussed. The energies calculated for this effect are of the order of 0·1 kcal/mol suggesting that for observable effects on curvature an array of such ligands will be needed. Some real systems in which this effect may be playing a role are discussed.     

Multivalent ligand–receptor binding on supported lipid bilayers

Fluid supported lipid bilayers provide an excellent platform for studying multivalent protein–ligand interactions because the two-dimensional fluidity of the membrane allows for lateral rearrangement of ligands in order to optimize binding. Our laboratory has combined supported lipid bilayer-coated microfluidic platforms with total internal reflection fluorescence microscopy (TIRFM) to obtain equilibrium dissociation constant (K_D) data for these systems. This high throughput, on-chip approach provides highly accurate thermodynamic information about multivalent binding events while requiring only very small sample volumes. Herein, we review some of the most salient findings from these studies. In particular, increasing ligand density on the membrane surface can provide a modest enhancement or attenuation of ligand–receptor binding depending upon whether the surface ligands interact strongly with each other. Such effects, however, lead to little more than one order of magnitude change in the apparent K_D values. On the other hand, the lipophilicity and presentation of lipid bilayer-conjugated ligands can have a much greater impact. Indeed, changing the way a particular ligand is conjugated to the membrane can alter the apparent K_D value by at least three orders of magnitude. Such a result speaks strongly to the role of ligand availability for multivalent ligand–receptor binding.     

The effect of iron-hexacyanide binding on the determination of redox potentials of cytochromes and copper proteins

The midpoint redox potentials of Pseudomonas aeruginosa cytochrome c-551 and Rhodopseudomonas viridis cytochrome c₂ were measured as a function of pH in the presence of Euglena cytochrome c-558 and the results compared with those obtained in the presence of ferro-ferricyanide. The pattern of pH dependence observed for the two bacterial cytochromes was the same whether it was measured by equilibrium with another redox protein or with the inorganic redox couple. Thus, the pH dependence of redox potential is not a consequence of pH-dependent ligand binding. The midpoint potential of Ps. aeruginosa azurin was measured as a function of pH using both ferro-ferricyanide mixtures and redox equilibrium with horse cytochrome c or Rhodopseudomonas capsulata cytochrome c₂. In this case also the pattern of pH dependence obtained did not vary with the redox system used and it closely resembled that of Ps. aeruginosa cytochrome c-551. This is consistent with the observation that the equilibrium between cytochrome c-551 and azurin is relatively independent of pH. An equation was derived which described pH-dependent ligand binding and which can produce theoretical curves to fit the experimental pH dependence of redox potential for both cytochrome and azurin. However, the pronounced effect on such curves produced by varying the ligand association constants, and the insensitivity of the experimental data to changes in ionic strength, suggest that ligand binding effects do not account for the pH dependence of redox potential.     

Cooperativity of ligand binding as a function of monomer-dimer equilibrium parameters and acceptor concentration

A general monomer-dimer equilibrium system involving ligand interactions ispresented. Cooperativity features of specific limited models are analyzed by selecting the appropriate family of equilibrium constants from this general scheme. Each system is then characterized in terms of Hill coefficient dependency on alterations in values of equilibrium constants and total acceptor concentration. This method permits comparison of predicted cooperativity trends between systems. Contrasting reports concerning cooperativity dependencies for certain defined equilibrium systems are compared and the discrepancies resolved. Characteristics of cooperativity binding patterns are shown to include symmetry about dimerization association constant values, both positive and negative cooperativity for a single set of parameters, and significant changes in cooperativity features with relatively small changes in equilibrium parameters.     

Calculation of diffusion-limited kinetics for the reactions in collision coupling and receptor cross-linking

Both enzyme (e.g., G-protein) activation via a collision coupling model and the formation of cross-linked receptors by a multivalent ligand involve reactions between two molecules diffusing in the plasma membrane. The diffusion of these molecules is thought to play a critical role in these two early signal transduction events. In reduced dimensions, however, diffusion is not an effective mixing mechanism; consequently, zones in which the concentration of particular molecules (e.g., enzymes, receptors) becomes depleted or enriched may form. To examine the formation of these depletion/ accumulation zones and their effect on reaction rates and ultimately the cellular response, Monte Carlo techniques are used to simulate the reaction and diffusion of molecules in the plasma membrane. The effective reaction rate at steady state is determined in terms of the physical properties of the tissue and ligand for both enzyme activation via collision coupling and the generation of cross-linked receptors. The diffusion-limited reaction rate constant is shown to scale with the mean square displacement of a receptor-ligand complex. The rate constants determined in the simulation are compared with other theoretical predictions as well as experimental data.     

Quaternary solution structures of galectins-1, -3, and -7

Galectins are a growing family of animal lectins with functions in growth regulation and cell adhesion that bind beta-Gal residues in oligosaccharides. Evidence indicates that some of the biological properties of galectins are due to their cross-linking activities with multivalent glycoconjugate receptors. Therefore determination of the quaternary solution structures of these proteins is important in understanding their structure-function properties. The present study reports analytical sedimentation velocity and equilibrium data for galectins-1, -3, and -7 in the absence and presence of bound LacNAc, the natural ligand epitope. Galectin-1 from bovine heart and recombinant human galectin-7 were found to be stable dimers by both methods. In contrast, recombinant murine galectin-3, as well as its proteolytical derived C-terminal domain, are predominantly monomeric. The presence of LacNAc at concentrations sufficient to fully saturate the proteins had no significant effect on either the weight average molecular weight determined by sedimentation equilibrium or the hydrodynamic properties determined from sedimentation velocity experiments. These results show that binding of a monovalent ligand does not affect oligomerization of these galectins.     

Selective immobilization of multivalent ligands for surface plasmon resonance and fluorescence microscopy

Cell surface multivalent ligands, such as proteoglycans and mucins, are often tethered by a single attachment point. In vitro, however, it is difficult to immobilize multivalent ligands at single sites due to their heterogeneity. Moreover, multivalent ligands often lack a single group with reactivity orthogonal to other functionality in the ligand. Biophysical analyses of multivalent ligand-receptor interactions would benefit from the availability of strategies for uniform immobilization of multivalent ligands. To this end, we report the design and synthesis of a multivalent ligand that has a single terminal orthogonal functional group and we demonstrate that this material can be selectively immobilized onto a surface suitable for surface plasmon resonance (SPR) experiments. The polymeric ligand we generated displays multiple copies of 3,6-disulfogalactose, and it can bind to the cell adhesion molecules P- and L-selectin. Using SPR measurements, we found that surfaces displaying our multivalent ligands bind specifically to P- and L-selectin. The affinities of P- and L-selectin for surfaces displaying the multivalent ligand are five- to sixfold better than the affinities for a surface modified with the corresponding monovalent ligand. In addition to binding soluble proteins, surfaces bearing immobilized polymers bound to cells displaying L-selectin. Cell binding was confirmed by visualizing adherent cells by fluorescence microscopy. Together, our results indicate that synthetic surfaces can be created by selective immobilization of multivalent ligands and that these surfaces are capable of binding soluble and cell-surface-associated receptors with high affinity.