Preferential ligand binding to multi-state acceptor systems: the unexplored paradox of acceptor self-association that is ligand-mediated but detrimental to ligand binding

Consideration is given to the interactions of ligand with self-associating acceptor systems for which preferential ligand binding is an ambiguous term, in that the acceptor species with greater affinity for ligand possesses relatively fewer binding sites. A paradoxical situation wherein ligand-mediated self-association is seemingly detrimental to ligand binding is shown to be the predicted outcome for a transient range of ligand concentrations. This outcome reflects the existence of a critical point in the dependence of the extent of acceptor self-association upon ligand concentration that coincides with a cross-over point of ligand-binding curves for different, fixed total concentrations of acceptor. By classical differentiation methods the conditions for the existence of these critical points are established not only for two-state acceptor systems but also for three-state acceptor systems in which the ligand-binding form of monomer also undergoes reversible isomerization to an inactive state. Similar procedures are used to comment upon the forms of binding curves for the three-state acceptor systems, the Scatchard representations of which may exhibit as many as three critical points (two maxima and a minimum). This delineation of quantitative expressions for critical points and other distinctive features associated with the conflicting interplay of ligand-binding and self-association behaviour should provide a more definitive means of characterizing systems with one acceptor state the preferred binding form on affinity grounds but with the other the preferred state from the viewpoint of binding-site numbers.     

The binding of a ligand to an acceptor undergoing indefinite self-association

Explicit expressions are derived which describe the binding of a univalent ligand to equivalent and independent sites on each state of an acceptor undergoing indefinite self-association that is governed by an isodesmic equilibrium constant KI. From considerations of systems in which the same site-binding constant kA applies to all acceptor-ligand interactions, the general forms of binding curves and Scatchard plots are deduced for situations in which binding sites are either created or lost at each monomer-monomer interface. Greater generality is then introduced into the model by allowing ligand interactions with polymeric acceptor states to be governed by a site-binding constant kp that differs in magnitude from that for monomeric acceptor kA. Finally, experimental results with the glutamate dehydrogenase-GTP and lysozyme-saccharide systems are used to illustrate ways in which the present quantitative expressions may be applied to the characterization of inteactions between a ligand and an indefinitely self-associating acceptor.     

An examination of the forms of scatchard plots of binding results outside domains of sigmoidality

General expressions are formulated for the first and second derivatives of the Scatchard function, r/[S], with respect to the binding function, r, from an equation that describes the binding of a ligand to a two-state acceptor system (either isomerizing or polymerizing). The expressions are utilized to determine the sign of the second derivative for particular systems under conditions where the first derivative is negative for all r. The work therefore correlates with previous studies, which stressed conditions of existence of critical points in Scatchard plots, by examining more fully possible forms of binding curves outside such domains of sigmoidality. Particular attention is given to the condition, d(r/[S])/dr < 0 and d²(r/[S])/dr² > 0 for all r (which defines a Scatchard plot convex to the r-axis). In agreement with previous findings it is proven that the isomerizing acceptor model cannot give rise to this form of plot and is therefore distinguished from negatively co-operative allosteric models. On the other hand, the polymerizing acceptor model may yield such a Scatchard plot, a feature demonstrated by formulating explicit conditions for its manifestation when ligand binding is exclusive to the polymeric state, and illustrated numerically for a system in which ligand binds to both oligomeric states. Distinction between such systems and those exhibiting negative co-operativity is possible on the basis of the Scatchard plots, which exhibit dependence on acceptor concentration in the case of a polymerizing acceptor; indeed, an example is provided where variation of acceptor concentration for a system characterized by fixed interaction parameters effects a conversion from sigmoidal binding behaviour to that typified by a Scatchard plot convex to the r-axis.     

The effect of ligand heterogeneity on the Scatchard plot. Particular relevance to lipoprotein binding analysis

Computer simulations of equilibrium binding studies of a mixture of two labeled ligands binding competitively to a single class of identical and independent sites (receptors) were performed to investigate how ligand heterogeneity affects the observed data in such studies. The simulated data are presented in Scatchard plots. Ligand heterogeneity was generally found to be indistinguishable from the case of a homogeneous ligand when usual experimental conditions applied (that is, Scatchard plots of the data were straight lines). Some factors that increased the probability of recognizing heterogeneity in the system were identified, however. These are 1) a large difference between the dissociation constants of the two ligands, 2) a high concentration of receptors relative to the dissociation constant of the higher-affinity ligand, 3) a high concentration of the lower-affinity ligand relative to that of the higher-affinity ligand, 4) a high specific activity of the lower-affinity ligand relative to that of the higher-affinity ligand, and 5) lack of experimental error. When ligand heterogeneity (under certain conditions) did cause curvilinearity in the Scatchard plot, the curve formed was always concave-downwards. Thus, ligand heterogeneity may occasionally mimic positive cooperativity, but never mimics negative cooperativity or multiple classes of binding sites. Implications of these findings for equilibrium binding studies involving lipoproteins (which are generally isolated as heterogeneous mixtures of particles) are discussed in detail. These findings are also relevant to equilibrium binding studies using ligands which are mixtures of stereoisomers or which contain chemical or radiochemical impurities.     

Ligand binding isotherm for DNA in the presence of supercoil-induced non-B form: a theoretical analysis

A binding isotherm in the form of a modified McGhee-Von Hippel equation is proposed, on the basis of thermodynamical considerations, to include the non-cooperative binding of extended ligands to supercoiled DNA, where a stretch of non-B form may be present under superhelical stress. It is then studied, on the basis of a non-linear Scatchard plot, how the presence of an intercalating ligand can relax the supercoiled molecule and thus destabilise the non-B stretch, which may be recognised by the existence of a significant kink in the Scatchard plot.     

On the analysis of linear binding effects associated with curved Scatchard plots.

First the question is examined as to which binding data, especially if given as Scatchard plots, can be described in terms of a basic model mechanism. This referes to a linear lattice of equivalent binding sites (as for example located on a linear biopolymer) which can exert cooperative interaction between nearest neighbors. It is shown that the effect of overlapping of potential site (so-called "multiple-contact"binding), as may occur with larger ligands, will largely be compensated by a higher degree of cooperativity. Therefore, in practice such properties can scarcely be separated by means of oridnary binding experiments. A pronounced inflection point in the Scatchard plot turns out to be clearly indicating a more complex mechanism involving at least two rather antagonistic cooperative interactions which may, however, occur even between equivalent binding sites. Finally some consequences of different classes of bindings sites are considered. In particular a simple approach is introduced by which the binding to mutually exclusive classes of sites may be described. Such a model is of interest for multiple-mode binding of ionic ligands to oppositely charged polymers.     

Interaction of vinblastine with calf brain tubulin: multiple equilibria

The binding of the anticancer drug vinblastine to calf brain tubulin was measured by a batch gel filtration method in PG buffer (0.01 M NaPi, 10(-4) M GTP, pH 7.0) at three different protein concentrations. The Scatchard binding isotherms obtained were curvilinear. The binding of the first vinblastine molecule to each tubulin alpha-beta dimer (Mr 110,000) was enhanced by an increase in the protein concentration. Additional binding of vinblastine to the protein was independent of the protein concentration. Theoretical ligand binding isotherms were calculated for a ligand-induced macromolecule self-association involving various ligand stoichiometries and association schemes. Fitting of the experimental data to these isotherms showed that the system can be described best by a one-ligand-induced isodesmic indefinite self-association. The pathway giving the best fit consists of a ligand-mediated plus -facilitated self-association mechanism. The self-association-linked bound vinblastine binds specifically at a site with an intrinsic binding constant K1 = 4 X 10(4) M-1. Additional vinblastine molecules can bind less strongly to tubulin in probably nonspecific fashion, and the previous reports of two specific sites on alpha-beta tubulin for binding vinblastine are incorrect. The self-association constant K2 for liganded tubulin is 1.8 X 10(5) M-1. This analysis is fully consistent with the conclusions derived earlier from the linked function analysis of the vinblastine-induced tubulin self-association [Na, G. C., & Timasheff, S. N. (1980) Biochemistry 19, 1347-1354; Na, G. C., & Timasheff, S. N. (1980) Biochemistry 19, 1355-1365].     

Identical independent sites for dye ligand on bovine serum albumin demonstrated by multivariate analysis

The most fundamental parameters concerning an interaction between a ligand and a protein are equilibrium constants and the number of binding sites. The Scatchard plot has for a long time been widely used to obtain those parameters. However, controversy in 1982-1983 over the reliability of this plot (the graphical estimation of the number of identical independent sites from the x-intercept) indicated that some methodologies other than the Scatchard plot are expected. Over the past decade, we have developed a method for applying multivariate analysis to the problem of determining spectral features of a ligand associated with a protein molecule. In principle, this method is based mainly on the computer-assisted adjustment of dissociation constants to an assumed reaction model. We discovered in this process that an n-parameter, introduced into an equation for calculating the amount of dye ligand bound to a protein, coincided with the number of identical independent sites, under a certain condition in principal factor analysis calculation. In this study, we established a new methodology for determining the number of identical independent sites using synthesized spectral series, and we then applied this method to a simple reaction system composed of bovine serum albumin (BSA) and bromocresol purple (BCP) anions. BSA was found to have two identical independent sites for BCP anions at pH 8.8.     

Some general aspects regarding the interpretation of binding data by means of a Scatchard plot

The question is quantitatively examined which general information can be obtained from experimental data of ligand binding to macromolecules if represented by a Scatchard plot. In particular, the curvature as well as the intercepts and slopes at both coordinate axes are analyzed assuming rather general conditions including cooperative behavior (with applications to some simplified cases of interest in practice). The results should provide a basis for attempts to elucidate the binding mechanism of a system encountered in experimental work.     

The binding of an indefinitely associating ligand to acceptor: consideration of monovalent ligand species binding to a multivalent acceptor

Currently available binding theory is extended to incorporate the concept of indefinite self-association of the ligand. Binding equations are formulated in closed form for the case of the binding to a multivalent acceptor of a ligand capable of isodesmically indefinitely self-associating in a "head-to-tail" mode such that each ligand state bears one site capable of interacting with the acceptor. It is shown both mathematically and by way of numerical example that this system will give rise exclusively to binding curves convex to the r-axis in Scatchard format. Thus, the system provides another example of a binding mechanism capable of generating an apparent negatively co-operative binding response.     

A Model for the Effect of Estrogen Antagonists on Cooperative Estradiol Binding

Abstract

Partial agonists such as estriol and estrone have been reported to diminish or even eliminate the upward convexity of the Scatchard plot of the binding of labeled estradiol to estrogen receptor. This has been interpreted as agonist interference with the receptor dimerization induced by estradiol. In order to investigate how a partial agonist or antagonist might interfere with dimerization we have developed a theoretical mass-action law model, where soluble receptors can dimerize and bind to two different ligands. Special attention was devoted to manifestations of positive cooperativity to determine whether they could be modified by competition with a second ligand. This was done using a computer program that evaluated a large set of combinations of affinity constants in an effort to explore all possible situations. The model could reproduce the effect of a second ligand on the cooperative binding of estradiol to the estrogen receptor but only if the second ligand was anticooperative, which is not the case of estriol, estrone and tamoxifen. Furthermore, even when the Scatchard plot was linear, the model still required dimerization of the receptor in most of the cases, showing that the addition of an antagonist may eliminate the upward curvature of the Scatchard without truly eliminating dimerization or cooperativity. We conclude that the effect of a second ligand on the binding of labeled estradiol to estrogen receptor is not necessarily due to interference with dimerization and/or cooperativity. The inability of this model to fully explain the published data for estriol, estrone, clomiphene, and tamoxifen suggests that a more complex mechanism is involved.     

Temperature-sensitive high affinity [3H]tryptamine binding sites in rat brain

The influence of prior incubation on [3H]tryptamine binding was investigated in rat brain synaptic plasma membranes. A 55 min preincubation of the membranes at 37 degrees C induced an approx. 2.4-fold increase in the specific binding of [3H]ligand to the subsequently washed preparations and this phenomenon was quite temperature-dependent. On the other hand, the proportion of nonspecific binding sites was significantly decreased by 70% of the original sites within 20 min of the start of preincubation. Pargyline, ascorbic acid, EGTA, metal ions (Ca2+, Mg2+, Na+) and guanine nucleotides, included in the preincubation buffer, were all inactive on the stimulation of [3H]tryptamine binding, while the pretreatment of membranes with glutaraldehyde antagonized the augmentation of this binding. Furthermore, it was revealed that the Scatchard plot of the [3H]tryptamine binding preincubated at 0 degree C conformed to a straight line (KD = 33.1 nM, Bmax = 543 fmoles/mg protein), whereas a curvilinear Scatchard plot was obtained at 37 degrees C preincubation. Nonlinear regression analysis of the latter resulted in apparent KD (nM) & Bmax (fmoles/mg protein) values of 0.45 & 102.7 and 33.7 & 603.4 for the high and low affinity sites, respectively. All these observations lead to the inference that the preincubation-induced increase in [3H]tryptamine binding (i.e., nearly high affinity proportion of sites) may occur as a result of temperature-sensitive interconvertible conformational changes.     

Hetero-association of caffeine and aromatic drugs and their competitive binding with a DNA oligomer

NMR spectroscopy has been used to elucidate the molecular basis of the action of caffeine (CAF) on the complexation with DNA of mutagens such as ethidium bromide, propidium iodide, proflavine and acridine orange, and anticancer drugs such as actinomycin D and daunomycin. The hetero-association of CAF and each of the aromatic ligands in 0.1 mol L(-1) phosphate buffer (pD=7.1) has been investigated as a function of concentration and temperature by 500 MHz 1H NMR spectroscopy and analysed in terms of a statistical-thermodynamic model, in which molecules form indefinite aggregates for both self-association and hetero-association. The analysis leads to determination of the equilibrium constants of hetero-association and to the values of the limiting chemical shifts of the heteroassociation of CAF with each of the aromatic molecules. The hetero-association constants between CAF and each of the aromatic drugs/dyes are found to be intermediate in magnitude between those for self-association of CAF and the corresponding drug/dye. The most probable structures of the 1:1 CAF + ligand hetero-association complexes have been determined from the calculated values of the induced limiting chemical shifts of the drug protons. Knowledge of the equilibrium constants for self-association of CAF and the aromatic ligands, for their hetero-association and their complexation with a DNA fragment, the deoxytetranucleotide 5'-d(TpGpCpA), enabled the relative content of each of the CAF-ligand and CAF-ligand-d(TGCA) complexes to be calculated as a function of CAF concentration in mixed solutions. It is concluded that, on addition of CAF to the solution, the decrease in binding of drug or mutagen with DNA is due both to competition for the binding sites by CAF and the aromatic molecules, and to formation of CAF-ligand hetero-association complexes in the mixed solution; the relative importance of each process depends on the drug or mutagen being considered.     

DNA bis-intercalation: Theoretical calculation of binding curves

A statistical mechanical calculation of the binding properties of DNA bis-intercalators is presented, based on the sequence-generating function method of Lifson. The effects of binding by intercalation of one or both chromophores of a bifunctional intercalating agent are examined. The secular equation for a general model that includes the effects of neighbor (nearest and non-nearest) exclusion and/or cooperativity in the binding of both singly and doubly intercalated ligands is derived. Numerical results for binding curves are presented for a more restricted model in which each type of bound ligand rigorously excludes its nearest neighbor and the total number of sites covered by a doubly intercalated ligand is variable. At low values of free ligand concentration bis-intercalation dominates the binding process, while at high value of free ligand concentration, intercalation of only one chromophore per ligand becomes significant due to the unavailability of contiguous free sites required for bis-intercalation. Also, depending on the binding parameters, the free energy of the system can be lowered by a loss of doubly intercalated ligands in favor of singly intercalated ones. Corresponding to this transition in binding mode, the average number of sites occupied by a bound ligand decreases from that characteristic of bis-intercalation to that characteristic of mono-intercalation as free ligand concentration increases. An analysis of Scatchard plots describing bis-intercalation is presented.     

Specific binding of a stable prostacyclin analogue (Iloprost) to rat oxyntic mucosa

It has been reported that prostacyclin (PGI2) is the predominant species of prostanoid in rat oxyntic mucosa. However since PGI2 is inactivated under physiological conditions it has not been possible to demonstrate specific PGI2 binding to the rat stomach. Therefore a stable PGI2 analogue, Iloprost, was chosen as ligand in this study. Binding of labelled Iloprost to the 20,000 xg homogenate fraction of rat oxyntic mucosa was specific, dissociable, saturable and dependent upon the temperature and time of incubation. Neither tritiated PGE2 nor 6 keto PGF1 alpha displayed any significant specific binding to rat stomach. A Scatchard plot of the equilibrium binding data for Iloprost was curvilinear and could be resolved into at least two binding sites. The average parameters determined from Scatchard analysis were: dissociation constants of 1.8 X 10(-11) M and 7.1 X 10(-8) M and corresponding binding site concentrations of 12.0 pmole/mg and 4800 pmoles/mg protein respectively. PGI2 was less potent than unlabelled Iloprost in displacing 3H-Iloprost from its binding site. The addition of PGE2 to the incubation medium resulted in an increase in 3H-Iloprost binding. It is concluded that rat oxyntic mucosa has specific binding sites for PGI2-like agents but not for either PGE2 or 6 keto PGF1 alpha.     

Study of the binding of thyroxine by thyroxine-binding prealbumin by a dialysis method using a fixed free concentration of ligand (author's transl)]

In order to study ligand-protein binding in solution, a dialysis method was used in which the free concentration of ligand can be controlled. The method has certain advantages and was applied to the binding of thyroxine by thyroxine-binding prealbumin, a system about which the results found in the literature are not in good agreement. From the isotherm drawn according to the Scatchard plot, it was found that thyroxine-binding prealbumin only presents a single binding site for thyroxine per molecule, the association constant being 1.7 . 10(8) M-1.     

Preferential ligand binding to multi-state acceptor systems: comparisons of the calcium-binding and dimerization characteristics of prothrombin and fragment 1.

Consideration is given to the interactions of a ligand with self-associating acceptor systems for which preferential binding is an ambiguous term in that ligand-mediated self-association does not necessarily imply a greater binding constant for polymeric acceptor--even in instances where binding sites are preserved in the self-association process. This dilemma is shown to arise in situations involving the binding of ligand to monomeric and polymeric forms of an acceptor that also coexist in equilibrium with inactive isomeric states. For example, the ten-fold increase in the measured dimerization constant for prothrombin Fragment 1 in the presence of a saturating concentration of Ca2+ ion may well reflect the existence of a 12% greater binding constant for the interaction of metal ion with dimeric acceptor. However, that result, as well as the detailed form of the sigmoidal binding curve, are also reasonably described by another extreme model in which the monomeric and dimeric forms of the acceptor possess equal affinities for Ca2+ ion. Likewise, the fact that the same experimental dimerization constant applies to prothrombin and its Ca(2+)-saturated complex does not preclude the possibility that the active form of dimeric zymogen exhibits a 12% greater affinity for metal ion. Numerical simulations have established that characterization of the dimerization behaviour as a function of free ligand concentration should allow greater discrimination between such models of the interplay between calcium binding and self-association of prothrombin and Fragment 1. Finally, by illustrating the likelihood that the disparity in self-association behaviour of prothrombin and Fragment 1 merely reflects minor differences in the relative magnitudes of isomerization constants and/or binding constants for monomeric and dimeric states of the two acceptors, the present investigation serves to allay concern about the validity of employing the proteolytic fragment as a model of the intact zymogen.     

A model for the association of intercalating ligands with mononucleosomes and chromatin

Scatchard plots in the literature on the association of ethidium bromide with mononucleosomes do not agree as to whether the association process is cooperative or non-cooperative or if the primary set of binding sites can be classified as strong or weak. A model is proposed in the present communication which appears to bring these conflicting studies into concert. The only assumption in this model is that a certain major fraction of the assumed potential binding sites are physically inaccessible to the binding of intercalating ligands as long as the mononucleosome is in its native conformation. It is argued that the nature of the Scatchard plot depends on the preparation of the sample, i.e. amount of DNA in the particle and whether or not the external histones H1 and H5 are present, since these quantities determine the amount of accessible DNA for inter-calating ligands. It is proposed that strong core histone-DNA contacts prevent access of intercalating ligands to ～ 120 base pairs of DNA in the core particle substructure of the nucleosome unit in the initial binding process and that additional ligand binding requires the disruption of these contacts. The model is generalized to the structure of whole chromatin and applied to oligonucleosome data.     

Experimental Artifacts and the Analysis of Ligand Binding Data: Results of a Computer Simulation

Abstract

Use of computerized analysis techniques for ligand binding data have recently become generally available, and are now used quite routinely. When used appropriately, these tools can improve the precision of the estimated parameters for binding affinity, K, and capacity, R. Furthermore, such programs can also calculate the uncertainty of the estimates e.g., as a percent coefficient of variation (%CV). However, because of unmeasured variability in specific activity, tracer purity, counting efficiency, counter background, efficiency of separation, etc., the actual uncertainty in the parameters K and R is usually much larger than stated. In an attempt to examine the effects of such artifacts, we have developed a computer program which simulates data arising from a number of commonly used experimental designs, and then intentionally distorted with each of these artifacts. Finally, the data are converted to B/F and B and plotted in the conventional Scatchard plot. Distortions revealed in this graph are indicative of the effect each artifact has on the parameter estimates. The computer program is generally written to simulate the binding of 2 or more ligands to one, two or many classes of independent or cooperative specific sites as well as to nonspecific sites. Thus, the program is applicable in a wide variety of situations. Results show that low tracer purity (“bindability”) or low filtration efficiency will significantly alter the measured R value. Poorly determined specific radioactivity may significantly alter the measured K value as well. Imprecise measurement of machine background may result in the specious appearance of positive cooperativity, or of additional high or low affinity classes of binding sites. Finally, under some circumstances, it is possible to detect and correct for the presence of these artifacts.     

Analysis of receptor binding displacement curves by a nonhomologous ligand, on the basis of an equivalent competition principle

An exact method for the analysis of receptor-ligand binding data when labeled bound ligand is displaced by a nonhomologous ligand with a different dissociation constant is described. The present method, which is based on an equivalent competition principle for the homologous and the nonhomologous ligand, converts displacement curves into a linear form and is also applicable to situations in which free concentrations of ligand are significantly smaller than the added concentrations as a result of ligand binding. It is shown that the dissociation constant of the nonhomologous ligand is given directly by the concentration of this nonhomologous ligand added and the free concentration of unlabeled homologous ligand required to give the same level of displacement of labeled bound ligand. On the basis of these displacement characteristics, all binding parameters for receptor interaction of the nonhomologous ligand can be obtained and expressed, for example, in a Scatchard plot. The present method, which is referred to as the equivalent competition method, is also evaluated in this study with respect to the effects of nonspecific ligand binding and the presence of multiple receptor classes.