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.     

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.     

Simulation of Association Curves and ‘Scatchard’ Plots of Binding Reactions Where Ligand and Receptor are Degraded or Internalized

Abstract

Frequently during the course of binding to a receptor, ligand is degraded. In some preparations receptor is degraded. And with isolated cell preparations, ligand and/or receptor may be internalized. Here we present a mathematical model in which the binding and other reactions are combined. The resulting set of differential equations is solved numerically to simulate association curves and the resulting values of bound and free ligand are used to construct Scatchard plots. Where non-ideal conditions exist, the Scatchard plots are generally curvilinear. Dependence of this curvilinearity - on time of measurement of free and bound ligand, on degradation and internalization of ligand, and on degradation and internalization of receptor - is shown. Equilibrium constants derived from the Scatchard plots are generally incorrect but the derived receptor concentration is often correct. The simulations suggest experimental possibilities for distinction among the several side reactions in ligand-receptor binding systems.     

Apparent “negative cooperativity” kinetics in the absence of a nonlinear Scatchard plot of thyrotropin-receptor interaction in a human thyroid adenoma

A human thyroid adenoma (benign nodule) was identified which exhibited a linear Scatchard plot of ¹²⁵I-TSH binding, characteristic of a single class of binding site with high affinity (K_d = 0.5±0.1 nM) and low binding capacity (0.8±0.2 pmol/mg protein). In contrast, Scatchard analysis of binding to adjacent normal thyroid was nonlinear, suggesting the presence of high and low-affinity binding sites with K_d's of 0.4±0.2 and of 27.9±11.0 nM and capacities of 0.7±0.3 and 1.8±1.0 pmol/mg protein, respectively. Dissociation of bound ¹²⁵I-TSH from membranes of both adenoma and normal tissue revealed identical enhancement of dissociation in the presence of excess native hormone, thought to be evidence for the “negative cooperativity” model of hormone-receptor interaction. Furthermore, adenylate cyclase from both tissues was equally responsive to TSH. Thus, a thyroid adenoma which contains TSH-responsive adenylate cyclase still exhibited enhanced dissociation by native hormone, even though Scatchard analysis yielded a single, non-cooperative class of binding sites. This suggests that enhanced dissociation of bound hormone does not provide a demonstration of negatively-cooperative site-site interaction. Furthermore, nonlinear Scatchard plots, typical of TSH binding in normal thyroid, represent two classes of binding sites, of which the high affinity type is responsible for stimulation of adenylate cyclase.     

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.     

Simulation of Association Curves and ‘Scatchard’ Plots of Binding Reactions where Ligand and Receptor are Degraded or Internalized

Abstract

Frequently during the course of binding to a receptor, ligand is degraded. In some preparations receptor is degraded. And with isolated cell preparations, ligand and/or receptor are internalized. Here we present a mathematical model for the combined binding and other reactions which gives useful information about the behaviour of such systems. The set of differential equations is solved numerically to simulate association curves and the resulting values of bound and free ligand are used to construct Scatchard plots. Where non-ideal conditions exist, the Scatchard plots are generally curvilinear. Dependence of this curvilinearity on time of measurement of free and bound ligand, on degradation and internalization of ligand and on degradation and internalization of receptor is shown. Equilibrium constants derived from the Scatchard plots are generally incorrect but the derived receptor concentration is often correct. The simulations lead to possibilities for distinction among the several side reactions in ligand-receptor binding systems.     

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.     

Thyrotropin receptors in normal human thyroid. Nonclassical binding kinetics not explained by the negative cooperativity model

Saturation analysis of equilibrium binding of iodinated thyrotropin (125I-TSH) to normal human thyroid preparations yielded linear Scatchard plots under non-physiological conditions of pH 6.0 or 20 mM Tris/acetate buffer, pH 7.4. The apparent equilibrium dissociation constant of this binding was approximately 10(-8) M. By contrast, nonlinear plots were obtained under standard conditions of pH 7.4 and 40 mM Tris/acetate buffer. Resolution of the components of these curves by computer analysis revealed the presence of at least two classes of binding sites, one of which is of a low capacity and high affinity (approximately 10(-10) M) consistent with receptor binding. The other component is of a high capacity and lower affinity. Binding to non-target tissues of muscle, parathyroid, mammary carcinoma, and placenta was only demonstrable at pH 6.0 or in 20 mM Tris/acetate buffer, pH 7.4, yielding linear Scatchard plots with similar binding affinity (approximately 10(-8)M) to normal thyroid but much reduced capacity. Preincubation of thyroid tissue at 50 degrees C resulted in an apparent selective loss of the high affinity component of binding measured under standard conditions. Kinetic experiments on the dissociation of bound 125I-TSH were undertaken to determine whether the non-linearity of Scatchard plots was due to two or more classes of binding sites or negative cooperativity. It was found that the experimental determinant that is presently ascribed to a negative cooperativity phenomenon regulating receptor affinity (i.e. an enhanced dilution-induced dissociation rate in the presence of excess native hormone), although apparently hormone-specific, was demonstrated under nonphysiological binding conditions and in non-target tissue. Significantly, the phenomenon was found under conditions of pH 6.0 or 20 mM Tris where a linear Scatchard plot was obtained. The evidence thus suggests that 125I-TSH binds to heterogeneous binding sites (of which the high affinity is probably the receptor for TSH) and that the enhanced dilution-induced dissociation of bound hormone by native hormone for this system, is only a characteristic of the low affinity binding site (maybe gangliosides).     

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.     

Ligand size as a determinant for catabolism by the low density lipoprotein (LDL) receptor pathway. A lattice model for LDL binding

Low density lipoproteins (LDL) are large (Mr = 2.5 x 10(6)) in comparison to LDL receptors (Mr = 115,000). Since most LDL receptors are clustered in coated pits, we tested the hypothesis that crowding of receptor-bound LDL particles would cause steric effects. The apparent affinity of LDL for receptors on cultured fibroblasts decreased near saturation causing concave-upward Scatchard plots. Both the higher and lower affinity components of binding were up-regulated by the cholesterol synthesis inhibitor, lovastatin, indicating that the entire binding curve was sterol-responsive. In contrast, neither component of LDL binding was present on lovastatin-treated or untreated null fibroblasts which are incapable of expressing LDL receptors. Therefore, the concave-upward Scatchard plots were entirely due to binding to LDL receptors. These results are consistent with a lattice model in which receptor-bound LDL are large enough to decrease binding to adjacent receptors. A lattice model implies that large LDL should produce steric effects at a lower receptor occupancy than should small LDL. This was tested using seven LDL fractions that differed in diameter from 20 to 27 nm. Fewer large than small LDL were bound to the cell surface at 4 degrees C and 37 degrees C, and fewer were internalized and degraded at 37 degrees C. Since large LDL bound via both apolipoprotein (apo) E and apoB100, receptor cross-linking could have caused fewer large LDL to be bound at saturation. However, when the potential for cross-linking was prevented by an apo-E-specific monoclonal antibody (1D7), the difference in binding by large versus small LDL was not eliminated; instead, it was exaggerated. Taken together, these results support a lattice model for LDL binding and indicate that steric hindrance associated with crowding of LDL particles on receptor lattices is a major determinant for catabolism by the LDL receptor pathway in vitro.     

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.     

Interaction of protein with a self-associating ligand. Deviation from a hyperbolic binding curve and the appearance of apparent co-operativity in the Scatchard plot

We derived a general formula to analyze a binding system in which a ligand self-associates, in terms of experimentally determinable quantities, i.e. r, the average number of bound ligands per protein molecule, and Lft, the total free ligand concentration, which are expressed as a ligand monomer unit. The limiting behaviors of the Scatchard plot (r/Lft vs r plot), that is, the intercepts on the r-axis and the r/Lft-axis, and the limiting slopes, are generally given. Three models that may be encountered are considered in detail. Numerical examples are also presented to illustrate how the self-association of a ligand affects the binding curves. The ligand self-association alone can cause deviation of the profile of the binding curve (r vs Lft plot) from a hyperbola, resulting in a nonlinear Scatchard plot. Therefore, analysis of the binding data without consideration of ligand self-association may lead to erroneous conclusions as to the numbers and classes of binding sites, co-operativity among the sites and binding parameter values.     

Purification of DT-diaphorase by affinity chromatography. Occurrence of two subunits and nonlinear Dixon and Scatchard plots of the inhibition by anticoagulants.

A new purification procedure based on affinity chromatography of rat liver DT-diaphorase on Sepharose-bound dicoumarol is described. The native enzyme has a molecular weight of 55,000 and contains 1 mol of flavin-adenine dinucleotide per mol of enzyme, in agreement with earlier reports. Sodium dodecyl electrophoresis sulfate-gel reveals the occurrence of two subunits of about equal molecular weight (27,000). Dixon plots of the inhibition of the native enzyme by either dicoumarol or 2-pivaloyl-1,3-indandione are nonlinear. Scatchard plots of dicoumarol binding in the absence or presence of other anticoagulants, (Warfarin and 2-pivaloyl-1,3-indandione) are also nonlinear. The nonlinear Dixon and Scatchard plots are interpreted as reflecting the existence of more than one inhibitor-binding site. The kinetic data are discussed in relation to the subunit structure of the enzyme.     

A model for cooperative ligand binding at complementary sites of DNA

The process of cooperative binding of ligands to DNA has been classified into different modes. An additional mode of cooperative interaction amongst ligands binding at sites on complementary strands has been emphasised. A statistical mechanical method has been applied to obtain an analytical expression for the fraction of nucleotide sites bound. Theoretical Scatchard plots have been drawn and analysed.     

Interaction of phenylthiolato-(2,2'',2"-terpyridine)platinum(II) cation with DNA.

The interaction between a novel aromatic thiolato derivative from the family of DNA-intercalating platinum complexes, phenylthiolato-(2,2',2"-terpyridine)platinum(II)-[PhS(ter py)Pt+], and nucleic acids was studied by using viscosity, equilibrium-dialysis and kinetic measurements. Viscosity measurements with sonicated DNA provide direct evidence for intercalation, and show that at binding ratios below 0.2 molecules per base-pair PhS(terpy)Pt+ causes an increase in contour length of 0.2 nm per bound molecule. However, helix extension diminishes at greater extents of binding, indicating the existence of additional, non-intercalated, externally bound forms of the ligand. The ability of PhS(terpy)Pt+ to aggregate in neutral aqueous buffers at a range of ionic strengths and temperatures was assessed by using optical-absorption methods. Scatchard plots for binding to calf thymus DNA at ionic strength 0.01 (corrected for dimerization) are curvilinear, concave upward, providing further evidence for two modes of binding. The association constant decreases at higher ionic strengths, in accord with the expectations of polyelectrolyte theory, although the number of cations released per bound unipositive ligand molecule is substantially greater than 1. Stopped-flow kinetic measurements confirm the complexity of the binding reaction by revealing multiple bound forms of the ligand whose kinetic processes are both fast and closely coupled. Thermal denaturation of DNA radically alters the shapes of binding isotherms and either has little effect on, or enhances, the affinity of potential binding sites, depending on experimental conditions. Scatchard plots for binding to natural DNA species with differing nucleotide composition show that the ligand has a requirement for a single G X C base-pair at the highest-affinity intercalation sites.     

DNA bis-intercalation: Application of theory to the binding of echinomycin to DNA

The statistical mechanical model for the binding of bifunctional intercalating ligands to duplex DNA described in the preceding paper is applied to the example of echinomycin–DNA interactions. This is the only system for which binding curves have been obtained under conditions leading to binding by both bis-intercalation and mono-intercalation simultaneously. Binding parameters and Scatchard plots are calculated for a variety of conditions. A detailed comparison of these calculations with the results from the previous analysis of the same binding data in terms of the McGhee-Von Hippel theory, assuming only one mode of binding, is presented. The results of our calculations are consistent with the model of bis-intercalation requiring the two bound chromophores of a bifunctional ligand to be separated by two base pairs. It is not necessary to assume violation of the nearest-neighbor exclusion principle, as occurred in the original analysis.     

Scatchard plot: Common misinterpretation of binding experiments

The widespread misinterpretation in the literature of ligand-protein binding experiments which show upward curvature in Scatchard plots is emphasized. The most commonly encountered errors are discussed and references to the correct methods of resolution of upward-curved Scatchard plots are given.     

Equilibrium dialysis and circular dichroic analysis of the novobiocin-bovine serum albumin complex.

The binding of the drug novobiocin by bovine serum albumin has been analyzed by Scatchard plots at two temperatures and three ionic strengths. In all cases the nonlinearity of the plots indicates heterogeneity of the combining sites on the protein, and an analysis of the changes observed in the circular dichroic spectra of the bound drug supports this observation. By use of a three-constant model the best fit for all of the parameters is achieved by assuming the initial site on the protein to be unique, the next five sites to be homogeneous, and subsequent binding to be described by a simple distribution between two phases. The temperature variation studies reveal that the first site derives its free energy of binding totally from a favorable change in entropy while the second class of five sites derives their free energy of binding from a favorable enthalpy change. Comparisons are made between the binding of novobiocin by bovine albumin and by human 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.     

Ouabain-receptor interactions in (Na+ + K+)-ATPase preparations. A contribution to the problem of nonlinear Scatchard plots.

Specific [3H]ouabain binding to rat and guinea pig skeletal muscle (musculus soleus) was studied using a rapid centrifugation and a filtration method. Both assays gave identical results: the incubation of the cell membranes in 50 mM imidazole/HCl buffer pH 7.25 or 7.4 MgCl2, Pi caused a time dependent loss of (Na+ +K+)-ATPase activity indicating an alteration of the membrane preparation. Ouabain binding properties were changed concomitantly. If ouabain binding was allowed to proceed until equilibrium was reached (3 min in rat and 10 min in guinea pig) at 37 degrees C the data plotted according to Scatchard followed a straight line. The dissociation constants of the ouabain-receptor-complexes of the rat cell membrane preparation as calculated from the slope of the plot (KD = 134 nM) and from the ratio of the dissociation and association rate constants (KD = 175 nM) agreed within experimental error with that determined by Clausen and Hansen [(1974) Biochim. Biophys. Acta 345, 387-404] in intact soleus muscles (KD = 210 nM). If ouabain binding was allowed to proceed for a longer period, however, nonlinear Scatchard plots resulted with an identical maximal number of binding sites but inconstant and decreased affinity for the cardiac glycoside. Experimental evidence is presented that nonlinear Scatchard plots often obtained in hormone (drug)-receptor binding experiments may (among other things) be the result of damaged cell membrane particles in vitro.