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.     

三齿草藤(Vicia bungei Ohwi)凝集素的细胞表面受体研究

应用亲和层析法从三齿草藤(Vicia bungei Ohwi)种子中纯化的三齿草藤凝集素(VBL),可以凝集兔和豚鼠的红细胞,也可凝集人、牛和羊的精细胞,说明这些细胞表面存在有VBL的受体。用FITC和~(125)I进行标记,可得到FITC-VBL和~(125)I-VBL,其生物学活性不受影响。氯胺T法的标记率可达55％;应用FITC-VBL研究牛精细胞和兔红细胞膜上VBL受体的分布,发现二者由胞膜上受体分布据不一致。VBL与牛精细胞结合条件的正交试验表明细胞浓度的影响最大。用不同量的未标记的VBL对~(125)I-VBL与兔红细胞和人精细胞的结合实验,以Scatchard法作图,兔红细胞得一类似于双曲线的凹形曲线,提示该细胞膜上受体的性质有所不同,而人精细胞却有很大差异。若以兔红细胞膜上存在有高低亲和力两种受体进行计算,可求得结合常数和每个细胞上的受体数。应用几种单糖和外源凝集素影响~(125)I-VBL与兔红细胞的结合,当单糖(D-Man,D-Glc)浓度为0.01M时,相对结合率开始急剧下降,单糖浓度若增至0.1M时,其相对结合率仅为40％,而PHA-P和SML浓度为1mg/ml时,相对结合率开始下降,当浓度达10mg/ml时,相对结合率下降至30％左右。     

Conditions for the existence of critical points in scatchard plots of binding results

An equation is presented in Scatchard format which describes the binding of a ligand to a two-state acceptor system (either isomerizing or polymerizing). It is used to formulate a general set of conditions for the existence of critical points in Scatchard plots and this set is explored in detail for particular cases. Explicit relations between the thermodynamic parameters governing the binding are thereby obtained which permit discussion of the boundaries of domains within which critical points may exist. Moreover, several items of evidence are presented which show that there is an exact correspondence between the appearance of critical points in Scatchard plots and points of inflexion in associated binding curves examples are presented where zero, one or more critical points and points of inflexion are observed. Finally, the effects on preferential binding of the variation of the environmental parameters, temperature and pressure (and for acceptor polymerization, the total acceptor concentration) are discussed in terms of the derived conditions of existence of critical points in Scatchard plots and their equivalent domains of sigmoidality of binding curves.     

Effect of the incomplete separation of bound and free ligand on binding measurements

An incomplete separation of free and acceptor-bound ligand causes underestimation of specific binding even though the determinations are corrected with blank or nonspecific binding values. If the failure of the experimental procedure causes contamination of bound ligand with free ligand, Scatchard plots are linear, though their slopes and abscissa intercepts are different from the true ones. On the other hand, if the ligand-acceptor complex is incompletely recovered, Scatchard plots are curvilinear with downward concavity. These problems can be overcome if the separable fractions of free and bound ligand are measured and suitable corrections are applied.The separation of free and receptor-bound ¹²⁵I-labeled human growth hormone by a precipitation method is taken as an example of the procedure.     

Irreversibility of the interaction of human growth hormone with its receptor and analysis of irreversible reactions in radioreceptor assays—Theoretical considerations

Kinetic studies of the binding and dissociation of [¹²⁵I]-human growth hormone to rabbit liver and mammary gland membrane receptors have showed that the binding of [¹²⁵I]-human growth hormone was largely irreversible to liver membrane receptors and completely to the solubilised mammary gland receptor. As Scatchard analysis assumes complete reversibility of the hormone-receptor interaction the validity of estimates of affinity and capacity of receptors derived by this analysis may be questionable. Theoretical considerations show that in unimolecular irreversible interactions of hormone and receptor, a nonlinear (concave) or a linear Scatchard plot can be obtained. In linear Scatchard plots the capacity of the receptor obtained by extrapolation represents an overestimation of true capacity. This overestimation correlates with the value of the intercept in the Scatchard plot.     

Implications of epidermal growth factor (EGF) induced egf receptor aggregation.

To investigate the role of receptor aggregation in EGF binding, we construct a mathematical model describing receptor dimerization (and higher levels of aggregation) that permits an analysis of the influence of receptor aggregation on ligand binding. We answer two questions: (a) Can Scatchard plots of EGF binding data be analyzed productively in terms of two noninteracting receptor populations with different affinities if EGF induced receptor aggregation occurs? No. If two affinities characterize aggregated and monomeric EGF receptors, we show that the Scatchard plot should have curvature characteristic of positively cooperative binding, the opposite of that observed. Thus, the interpretation that the high affinity population represents aggregated receptors and the low affinity population nonaggregated receptors is wrong. If the two populations are interpreted without reference to receptor aggregation, an important determinant of Scatchard plot shape is ignored. (b) Can a model for EGF receptor aggregation and EGF binding be consistent with the "negative curvature" (i.e., curvature characteristic of negatively cooperative binding) observed in most Scatchard plots of EGF binding data? Yes. In addition, the restrictions on the model parameters required to obtain negatively curved Scatchard plots provide new information about binding and aggregation. In particular, EGF binding to aggregated receptors must be negatively cooperative, i.e., binding to a receptor in a dimer (or higher oligomer) having one receptor already bound occurs with lower affinity than the initial binding event. A third question we consider is whether the model we present can be used to detect the presence of mechanisms other than receptor aggregation that are contributing to Scatchard plot curvature. For the membrane and cell binding data we analyzed, the best least squares fits of the model to each of the four data sets deviate systematically from the data, indicating that additional factors are also important in shaping the binding curves. Because we have controlled experimentally for many sources of receptor heterogeneity, we have limited the potential explanations for residual Scatchard plot curvature.     

Interactions between micellar ligand systems and acceptors: Forms of binding curves

A previously formulated expression describing the competitive binding to an acceptor of two states of a ligand, monomeric and polymeric, coexisting in equilibrium is examined in terms of the different forms of Scatchard plots which may arise in cases of exclusive and of preferential binding of the ligand states. It is shown by differentiation of the binding equation written in Scatchard format, and by numerical examples, that exclusive binding of the monomeric form of ligand leads to Scatchard plots that are either sigmoidal or convex to the abscissa, whereas exclusive binding of the polymeric form results in plots concave to the abscissa and exhibiting a maximum. Particular attention is given to Scatchard plots which possess two critical points, a situation which is shown to be possible when the polymeric form of ligand binds preferentially (but not exclusively) to the acceptor. The two-state ligand concept is especially pertinent to solutes capable of globular micelle formation and several examples are cited of binding studies which have been conducted with such micellar systems. Of these, the chlorpromazine-brain tubulin system is given detailed consideration in order to illustrate the use of the present theory in describing the binding results which exhibit two critical points when plotted in Scatchard format.     

Influence of carbachol on the kinetic parameters of the contractile response to noradrenaline in the rat vas deferens

Graphic and mathematical analysis of kinetics of the rat vas deferens contractile response to noradrenaline showed that alpha1-adrenoceptors mediating the contraction were in different functional states. In some organs, these receptors were homogeneous with the Hill coefficient n = 1 (the linear mode of the Scatchard plot), in the others--not homogeneous, with n > 1 (not linear mode of the Scatchard plot). Carbachol increased the contractile response to noradrenaline. As in the control, two types of response were revealed: 1. The Hill coefficient n < 1 (biphasic mode of the Scatchard plot) with two pools (high and low affinity) of alpha1-adrenoceptors, and 2. The Hill coefficient n = 1 (the linear mode of the Scatchard plot). These results suggest that the influence of carbachol is caused by the local interaction of M-cholinergic and alpha1-adrenergic systems.     

Effects of ligand multivalency in binding studies: a general counterpart of the Scatchard analysis

A general counterpart of the Scatchard analysis has been developed which takes into account the valence of the ligand. Its use is first demonstrated by application to binding data obtained by exclusion chromatography of mixtures of Dextran T2000 and concanavalin A (a bivalent ligand) on a column of porous glass beads (Glyceryl-CPG 170) equilibrated at 5 degrees C with phosphate-chloride buffer (pH 5.5), I 0.5. A recycling partition equilibrium study with Sephadex G-100 as gel phase then provides a quantitative evaluation of the interaction between haemoglobin and a monoclonal mouse antihaemoglobin antibody preparation in 0.1 M phosphate (pH 7.0) in order to emphasize the ability of the present analysis to consider collectively binding results obtained with a range of acceptor concentrations. Finally, the use of the generalized Scatchard analysis to assess acceptor site homogeneity is illustrated by reappraisal of results for the binding of glyceraldehyde-3-phosphate dehydrogenase to erythrocyte membranes.     

Binding of hormones to receptors. An alternative explanation of nonlinear Scatchard plots.

Binding of 1251-labeled hormones to receptors can usually be inhibited by addition of unlabeled hormone. In analyzing such binding-inhibition data, it is commonly assumed that both labeled and unlabeled hormones are bound with equal affinity. When this assumption is made incorrectly, an artifactually nonlinear Scatchard plot results. Equations to describe these nonlinear Scatchard plots are derived. These results are discussed with regard to previously published observations of nonlinear Scatchard plots for binding of insulin to its receptor.     

Binding of physostigmine to rat and human plasma and crystalline serum albumins

The binding of 3H-physostigmine (3H-Ph) to human and rat plasma proteins and crystalline serum albumin was studied by ultrafiltration technique. This study showed that the percentage of 3H-Ph bound to rat plasma slightly decreased from 49% to 41% whereas human plasma showed an increase in binding from 29% to 43% over a 50-fold increase in drug concentration. Human plasma samples which were collected in a bag coated with citrate phosphate dextrose adenine-1 solution bound 50% less 3H-Ph than samples collected with EDTA indicating a drug-drug interaction between 3H-Ph and anticoagulants. No significant change in binding was observed if the samples were frozen prior to use. Scatchard plots for binding of 3H-Ph resulted in a positive slope for human plasma and a negative slope for rat plasma; whereas curvilinear Scatchard plots with negative slopes were obtained for binding to human and rat crystalline serum albumin.     

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.     

Interactions of antibiotics of the iturin group with human erythrocytes

The peptidolipid antibiotics, iturin A and bacillomycin L have a disrupting effect on erythrocyte membrane leading to a simultaneous release of K+ ions and hemoglobin. The formation of ghosts is accompanied by a partial solubilisation of lipid components. Binding experiments with radioactive antibiotics show that about 7 X 10(7) molecules of iturin A and 4 X 10(7) molecules of bacillomycin L are bound to one erythrocyte at the concentration giving 100% hemolysis. This concentration is reduced by about 20% after treatment of erythrocytes by phospholipase A2. Scatchard plots show that the affinity for erythrocyte membrane is higher with bacillomycin L than with iturin A. This difference is probably correlated to the differences in their peptide moieties. The substitution of tyrosyl residue leads to a ten-fold increase of the concentrations giving 100% hemolysis, probably due to a low distribution coefficient of derivatives between the membrane and the solvent. This result and the humped Scatchard curves obtained with both antibiotics may be related to the self-association of the compounds in aqueous solutions.     

Estradiol- and estriol-binding in human benign prostatic hyperplasia.

Binding of the natural estrogens, estradiol and estriol, was investigated, in 34 samples of human benign prostatic hypertrophy (BPH) tissue, using Scatchard analysis and agar gel electrophoresis. Saturation binding analysis using a wide range of concentrations of both ligands resulted in curvilinear Scatchard plots. This confirmed the presence of two binding forms for estradiol: a true estrogen receptor, and a protein with lower affinity and higher capacity. Both binding species were also demonstrated and quantified with estriol. The electrophoretic process, after incubation at low and high ligand concentrations also resulted in separation, for both estrogens, of two binding peaks. They are probably two distinct forms of the low affinity, high capacity binding measured by Scatchard. The procedure used in our laboratory was not able to provide accurate determination of the concentrations of these binding forms. Possible modifications to alleviate these drawbacks are discussed.     

Effects of ligand multivalency in binding studies: a general counterpart of the Scatchard analysis

A general counterpart of the Scatchard analysis has been developed which takes into account the valence of the ligand. Its use is first demonstrated by application to binding data obtained by exclusion chromatography of mixtures of Dextran T2000 and concanavalin A (a bivalent ligand) on a column of porous glass beads (Glyceryl-CPG 170) equilibrated at 5°C with phosphate-chloride buffer (pH 5.5), I 0.5. A recycling partition equilibrium study with Sephadex G-100 as gel phase then provides a quantitative evaluation of the interaction between haemoglobin and a monoclonal mouse antihaemoglobin antibody preparation in 0.1 M phosphate (pH 7.0) in order to emphasize the ability of the present analysis to consider collectively binding results obtained with a range of acceptor concentrations. Finally, the use of the generalized Scatchard analysis to assess acceptor site homogeneity is illustrated by reappraisal of results for the binding of glyceraldehyde-3-phosphate dehydrogenase to erythrocyte membranes.     

Competitive interactions at [3H]1,3-di(2-tolyl)guanidine (DTG)-defined sigma recognition sites in guinea pig brain.

In saturation binding experiments, (+)pentazocine, (+)3-(3-hydroxyphenyl)-N-propylpiperidine (3-PPP), haloperidol and rimcazole did not inhibit the binding of [3H]DTG in a purely competitive fashion. Although Scatchard analysis indicated that [3H]DTG bound to a single site, the inhibition curves of some, but not all, reference compounds exhibited Hill coefficients of less than 0.8. The Scatchard data were consistent with a model of hyperbolic competitive inhibition of binding to the [3H]DTG-defined sigma site, although other possibilities such as negative cooperativity or binding to two sites cannot be definitively excluded. Compounds from numerous pharmacological and structural classes inhibited the binding of [3H]DTG, suggesting that interactions of [3H]DTG with other receptors may have confounded the Scatchard analysis of the binding of [3H]DTG to sigma recognition sites.     

Binding cross-reactivity of Boc-phenylalanine enantiomers on molecularly imprinted polymers

A potential problem associated with molecularly imprinted polymer (MIP) sorbents is that of cross-reactivity. In this study three MIPs (imprinted with Boc-L-phenylalanine, Boc-L-alanine, Boc-L-glutamic acid) plus a non-imprinted control were prepared and examined for their ability to bind differentially the enantiomers of boc-protected phenylalanine in an effort to quantify cross-reactivity and to develop a predictive model. Batch rebinding studies showed a degree of predictability for a number of MIP-ligand pairs, but other combinations showed unexpectedly high levels of cross-reactivity. Despite the general acceptance of heterogeneity of MIP binding sites, many previous studies report linear Scatchard plots, which is indicative of binding site homogeneity. The data from this study produced curves, clearly demonstrating heterogeneity. The theoretical and practical implications of this heterogeneity are discussed. Chirality 9:233–237, 1997. © 1997 Wiley-Liss, Inc.     

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

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

Phenylmethylsulfonyl fluoride (PMSF) inhibits 17 beta-estradiol binding to estrogen receptor from human prostate

Estrogen receptor binding studies were performed on cytosol obtained from human benign prostatic hyperplasia (BPH) tissue. Binding assays were done in the absence or presence of various concentrations of phenylmethylsulfonyl fluoride (PMSF). Saturation analysis and Scatchard plots showed that the binding of 17 beta -estradiol to the estrogen receptor (ER) was inhibited by PMSF. The nature of the inhibition appears to be uncompetitive, as determined from double-reciprocal plots. Glycerol density gradient centrifugation analysis also confirmed the results obtained with Scatchard plots. The inhibition observed in the presence of dithiothreitol (DTT) was greater than the inhibition observed in the absence of DTT. The maximum number of binding sites (Bmax) observed in our present study was 59.1 +/- 34.1 fmol/mg protein with an equilibrium dissociation constant (KD) of 2.2 +/- 2.2 nM. Our study indicates that PMSF significantly affects 17 beta -estradiol binding to ER and consequently alters the estimation of ER in Human BPH.     

Heterogeneities in EGF receptor density at the cell surface can lead to concave up scatchard plot of EGF binding

The mechanism responsible for the concave up nature of the Scatchard plot of epidermal growth factor (EGF) binding on EGF receptor (EGFR) has been a controversial issue for more than a decade. Past efforts to mechanistically simulate the concave up nature of the Scatchard plot of EGF binding have shown that negative cooperativity in EGF binding on an EGFR dimer or inclusion of some external site or binding event can describe this behavior. However, herein we show that heterogeneity in the density of EGFR due to localization in certain regions of the plasma membrane, which has been experimentally reported, can also lead to concave up shape of the Scatchard plot of the EGF binding on EGFR.