Ligand-receptor interactions: a new method for determining the binding parameters

A new experimental procedure and new plot coordinates that allow determination of the binding parameters of ligand-acceptor interaction have been proposed. Instead of titration of a constant concentration of receptors with changing concentrations of ligand, as requested by the well-known methods of Klotz and Scatchard, a series of sequential dilutions of the reacting ligand-receptor mixture is suggested. This allows the application of a new coordinate system that transforms the binding isotherms into straight lines. The case of one acceptor with two classes of receptors with different binding constants is also considered briefly, where the correspondent graphs are nonlinear. It is suggested that in some cases this approach can be a simple and convenient substitute of the broadly used methods of Klotz and Scatchard.     

Analysis of some "insoluble" problems of determining the binding parameters of ligand-receptor interaction and methods of their solving

Some problems of the estimation of the parameters of ligand-receptor interaction (affinity, rate constants, valency, etc.) were considered. It was demonstrated that not only the Scatchard plot but also Klotz plot could be used for determining the parameters of ligand-receptor interaction for two types of binding sites of different affinity. A new approach and new coordinate systems for the estimation of the parameters of ligand-receptor interaction were suggested. It was shown that for the estimation of the affinity of putative monovalent antibodies by ELISA various equations, which are more precise and convenient than the Friguet et al. equations, could be obtained by the transformation of mass action law equation. The problem solution for the estimation by ELISA the affinity of two types of bivalent antibodies with different affinity and their concentrations for the case of the mixture of these antibodies was also suggested. The application of the proposed coordinate of dilution allows to solve the problem of determination of the parameters of ligand-receptor interaction (including antigen-antibody system) for the pre-existing ligand-receptor mixture without their preliminary separation and purification. This approach is especially important for the cases when the receptor is not stable enough to be isolated in the intact form from this mixture. It was shown that the well-known phenomenon of the prozone often observed under the titration of serum antibodies by the method of agglutination may get a mathematical explanation. Analytical solution of the problem of determining the velocity constant and the amount of the end product of the first order irreversible and reversible reaction kinetics was suggested, despite the fact that the process is described by the system of irrational equations. Mehods of asymptotic solution of transcendental irrational equations which describe the dynamics of reactions which mechanisms are subject to the so-called heterogeneous, successive, or competitive models have been considered. These methods permit the finding of the reaction rate constants and the amount of the end product, if the kinetics of the transformation of either initial, or end product of the reaction is known.     

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.     

Two techniques for evaluating small molecule-macromolecule binding in complex system

Two techniques are proposed for the evaluation of multiple binding in complex systems. These techniques can be applied to reactions where more than one class of binding sites is present or where there are interactions between equivalent sites. The first technique employs a Klotz or Scatchard plot to evaluate three stoichiometric binding constants and the total number of sites. Furthermore the individual site binding parameters can be determined for several very important systems such as a macromolecule with two classes of independent sites or a macromolecule with three sites that are equivalent but not independent. For a system with many classes of independent sites, a second technique employs a continuous distribution of binding constants to analyze the reaction. This method does not require the assumption of a functional form for the distribution or a knowledge of the number of classes.     

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).     

Graphical analyses on binding of ligands to a two-sited system. Theoretical treatments exemplified on yeast phosphoglycerate kinase

Equilibrium studies on ATP^4? and 3-P-glycerate binding to phosphoglycerate kinase (ATP:3-phospho-d-glycerate 1-phosphotransferase, EC 2.7.2.3) have been performed. The results show that the enzyme contains two binding sites for both ligands, as was earlier suggested to explain some of the kinetic results. As long as structural information is lacking analysis of binding data can be analyzed if assumptions are made whether the sites are equivalent or nonequivalent, and whether ligation of these sites is mutually dependent or not. To understand the experimental results explicit expressions were derived for the limiting slopes and intercepts of Klotz and Scatchard plots, respectively, in terms of the intrinsic affinity constants valid under the separate assumptions made. The algebraic expressions for the limiting slopes were analyzed in order to ascertain the relationship between the form of these graphical plots, the prevailing types of binding site, and the intrinsic affinity constants. The results show that in case the equivalence of the binding sites is questionable it is necessary to be careful when the type of interaction is being determined. In certain cases it might be difficult to distinguish between positive and negative interaction. Sites that appear to be equivalent and independent could equally well be nonequivalent and dependent.     

Effect of FGF-1 and FGF-2 on VEGF binding to human umbilical vein endothelial cells

When FGF-1 or FGF-2 and VEGF were added together, the mitogenic effect of FGF-1 or FGF-2 and VEGF on HUVEC was additive. However, when HUVECs were preincubated for 2 days with 10 ng/ml FGF-1 in the absence of VEGF, the Scatchard plot of [125I]VEGF binding sites was shifted to the right: both affinity classes of VEGF binding sites were equally affected, such that the total number of sites increased twofold. It is suggested that this type of interaction may be related to tumor angiogenesis and wound repair.     

Metabolism-independent binding of toxic metals by Ulva lactuca: cadmium binds to oxygen-containing groups, as determined by NMR

The metabolism-independent metal binding characteristics of Ulva lactuca were investigated using both freeze-dried thalli and cell walls stripped of intracellular material by incubation in Triton-X followed by methanol. Biosorption of Cd, Zn, Cu and Co by freeze-dried thallus was concentration-dependent and followed Freundlich and Langmuir isotherms. The Freundlich plot suggested that freeze-dried U. lactuca had the greatest binding affinity for Cu compared with Cd, Zn and Co. The BET (Brunauer–Emmett–Teller) plot, which indicates a more complex form of adsorption, and the Scatchard plot were not adequate models for Cu adsorption. The Scatchard plot of Cd suggested that two Cd binding sites were available on the freeze-dried thallus, with the second, lower affinity site only becoming available at Cd loading capacities greater than 4.9mmol g dry wt. Cd nuclear magnetic resonance (NMR) studies confirmed that two binding sites were available for Cd on the freeze-dried algal powder, though only one was available on the cell wall, and that the affinity of the binding sites was greater for Cu than for Cd. The results of the NMR experiments suggested that Cd binds to oxygen-containing functional groups in the algal powder and on the cell wall. It is proposed that sulphate or hydroxyl groups attached to polysaccharide subunits are possible sites.     

A critical interpretation of experiments of binding of peptide hormone to specific receptors by computer modelling

Many investigations dealing with the interaction of peptide hormones and specific cell membrane receptors imply the existence of two classes of independent binding sites. One class is characterized by high affinity and low capacity, the other one by low affinity and high capacity. This conclusion has been derived from the fact that the Scatchard plots of binding data show a significant upward curvature. Using a more precise and critical method of evaluation these findings probably must be revised in some cases. Other conclusions taken from linear plots concerning the regulation of hormone receptors should be discussed more carefully. Some sources of errors caused by an uncritical interpretation of Scatchard plots are demonstrated.     

Evidence of high and low affinity binding sites for basic fibroblast growth factor in mouse placenta

The placenta has been shown to contain bFGF, but the presence of specific binding sites for this growth factor in this tissue remained to be established. In order to study the role of bFGF in the placenta growth, we looked for specific binding sites on mouse placental cell membranes at days 12, 14, 16, and 18 of pregnancy. At day 12, Scatchard analyses indicated that two classes of specific interaction sites for bFGF were detected. One class of high affinity binding sites was characterized by an apparent Kd of 10 pM and a binding capacity of 10 fmoles per mg of membrane protein. A second class of low affinity binding sites was detected with an apparent Kd of 60 nM and a binding capacity of 26 pmoles per mg of membrane protein. At days 14, 16 or 18, Scatchard analyses only showed low affinity binding sites with an apparent Kd of 24 nM and a binding capacity of 230 pmoles per mg of membrane protein. The characterization of these binding sites was performed by cross linking experiments that revealed two forms of specific complexes. This result suggested that the high affinity binding sites correspond to putative receptors with relative molecular masses equal to 65,000 and 85,000. The dramatic decrease of the high affinity receptor number after the 12th day of pregnancy, which is synchronous with the 9-fold increase of the low affinity binding site number, suggests that the biological activity of bFGF could be regulated by a balance between both the numbers of high and low affinity binding sites on placenta cell membranes. Thus, as it was shown for other growth factors, bFGF could only be involved at specific pregnancy stages.     

Reply to Claudio Cobelli and Gianna Toffolo,identifiability from parameter bounds. Structural and numerical aspects. Math. Biosci. 71:237–243 (1984)

We present an analysis of receptor mediated endocytosis which includes the following elements: ligand binding to receptors, interaction of the ligand-receptor complex with coated pits, internalization of coated pit contents, recycling of receptors, and degradation of ligand. The model accounts quantitatively for epidermal growth factor binding and clustering in coated pits at 4°C, for its internalization and degradation at 37°C, and for EGF receptor down-regulation. Steady state analysis of the model indicates that the slope and intercept of a Scatchard plot are functions of the kinetic parameters of the endocytic loop and do not necessarily reflect the affinity and number of receptors in metabolically active cells. Moreover, the model predicts that for homogeneous receptors, a Scatchard plot can be either linear or nonlinear, depending on the concentration of proteins in coated pits which interact with ligand-receptor complexes. A slight generalization of the model in which phorbol ester-receptor complexes compete with EGF-receptor complexes for the same coated pit proteins provides a quantitative explanation for the loss of the high affinity portion of the EGF Scatchard plot subsequent to preincubation with phorbol esters. This explanation leads to the prediction of a local homology between a portion of the phorbol ester receptor sequence and a portion of the EGF receptor sequence.     

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.     

The Ca2+ binding to deionized monomerized and to retinal removed bacteriorhodopsin.

In our continuing effort to characterize the metal cation binding in bacteriorhodopsin (bR) using Ca(2+)-specific electrodes, potentiometric titration was carried out on deionized solubilized bR (containing monomeric units) and deionized bacterioopsin (bR with its retinal removed). Scatchard plots were analyzed. The monomer was found to have plots similar to those of the trimer, suggesting that the binding sites in bR are localized within the protein monomer unit and not between the molecules within the trimer structure. This also supports the previous assumption that the curvature in the Scatchard plot of regenerated bR is not due to cooperativity of metal cation within the trimer, but rather due to multiple sites. Recent studies further support the finding that the curved Scatchard plot is not due to the cooperativity between the metal ions in the two high affinity sites, wherever they are. The results of the analysis of the Scatchard plot for deionized bacterioopsin have shown a change in the binding characteristics of the high affinity but not the low affinity sites from that observed in bR. This result supports previous conclusions that metal cations in the high affinity sites are not far from the retinal cavity.     

Theory of hapten binding to IgM: the question of repulsive interactions between binding sites.

Various workers in their studies of the binding of haptens to IgM have observed that at low hapten concentration IgM has an apparent valence of five or near five, while at high hapten concentration IgM has a valence of ten. A possible explanation for this is that there is an interaction between binding sites on the same F(ab')2 region of the IgM molecule. In this paper the theory for such an interaction is presented and an expression for the apparent valence is derived. It is shown that the apparent valence depends on both the interaction between binding sites on the IgM molecule and on the width of the affinity distribution which characterizes the antiserum. A broad affinity distribution can give an apparent valence of five even when there is no interaction between sites, i.e., even when the ten binding sites on the IgM molecule are identical and independent. The general properties of a Scatchard plot are also discussed. When there is no interaction between sites it is shown that the average affinity and the variance of the affinity distribution can be obtained from a Scatchard plot. To illustrate the theory, an antiserum with affinities characterized by a normal distribution is considered and a simple method is presented for determining alpha, the parameter which measures the width of the normal distribution.     

A derivative of befunolol, BFE-55, interacts with only the high affinity sites in beta-adrenoceptors

The effect of BFE-55, a derivative of befunolol (a beta-adrenergic partial agonist) on specific [3H]befunolol binding to a microsomal fraction from the guinea pig taenia caecum was tested. A Scatchard plot of specific [3H]befunolol binding in the absence of BFE-55 was concave, suggesting an existence of high and low affinity sites in beta-adrenoceptors. In contrast, the Scatchard plot of data in the presence of BFE-55 (3 X 10(-7) M) was straight. In the presence of BFE-55, the high affinity sites disappeared and the low affinity site was unaffected. In the absence and presence of BFE-55 there was no difference between the pKD values or Bmax values at the low affinity site. These findings indicate that BFE-55 interacts with only the high affinity sites in beta-adrenoceptors.     

The effects of human low and high density lipoproteins on the binding of rat intermediate density lipoproteins to rat liver membranes

Upon incubation with rat liver membranes, radioiodinated rat intermediate density lipoproteins (IDL) interacted with at least two binding sites having a low and a high affinity as demonstrated by the curvilinear Scatchard plots obtained from the specific binding data. The purpose of our work was to identify the nature of these binding sites. Human low density lipoproteins (LDL), contain apolipoprotein B only, and human high density lipoproteins (HDL3), containing neither apolipoprotein B nor E, were both capable of decreasing the specific binding of rat 125I-IDL. The Scatchard analysis clearly revealed that only the low affinity component was affected by the addition of these human lipoproteins. In fact, the low affinity binding component gradually decreased as the amount of human LDL or HDL3 increased in the binding assay. At a 200-fold excess of human LDL or HDL3, the low affinity binding was totally masked, and the Scatchard plot of the specific 125I-IDL binding became linear. Only the high affinity binding component was left, enabling a precise measurement of its binding parameters. In a series of competitive displacement experiments in which the binding assay contained a 200-fold excess of human LDL or HDL3, only unlabeled rat IDL effectively displaced the binding of rat 125I-IDL. We conclude that the low affinity binding of rat IDL to rat liver membranes is due to weak interactions with unspecified lipoprotein binding sites. The camouflage of these sites by human lipoproteins makes possible the study of IDL binding to the high affinity component which likely represents the combined effect of IDL binding to both the remnant and the LDL receptors.     

Binding of vasoactive intestinal polypeptide (VIP) by human blood monocytes: demonstration of specific binding sites

Vasoactive intestinal polypeptide (VIP) interaction with a 94% pure preparation of monocytes isolated from human peripheral blood was studied by direct binding technique using 3-[125I]tyrosyl-VIP as a tracer ligand. Scatchard analysis of binding data was compatible with two classes of binding sites, one with Kd = 0.25 nM and maximal binding capacity of 16 fmol/10(6) cells, and another one with Kd = 25 nM and maximal binding capacity of 180 fmol/10(6) cells. The binding was time-, temperature-, and pH-dependent and was saturable, reversible, and specific. This study has demonstrated that human monocytes have high affinity/low capacity as well as low affinity/high capacity binding sites for VIP. No specific VIP binding was found in pure preparations of human granulocytes, platelets or erythrocytes.     

Influence of molybdate, ionic strength and pH on ligand binding to the glucocorticoid receptor

The addition of molybdate to rabbit liver cytosol increased significantly the affinity of the glucocorticoid receptor for [3H] dexamethasone without influencing the concentration of binding sites. This effect was concentration dependent. Analysis of the binding data by curve-fitting and Scatchard plot revealed the occurrence of a complex binding process in the presence of molybdate. The pH-dependence curve of the binding was shifted towards alkaline values by the oxyanion. Taken together, these data suggest that molybdate exerts its effects via an interaction with the receptor molecule.     

Pharmacological characterization of two specific binding sites for neurohypophyseal hormones in hippocampal synaptic plasma membranes of the rat

Synaptic plasma membranes containing binding sites for tritiated oxytocin and arginine vasopressin were isolated from rat hippocampus. The binding parameters for oxytocin and vasopressin sites were determined and statistically analysed. The fitted curve for oxytocin binding was compatible with a model where the ligand interacts with two classes of receptors with different capacities and affinities. The sites with low binding capacity had an apparent dissociation constant at equilibrium of 1.8 nM and a maximal binding capacity of 17 fmol/mg protein. By contrast, the Scatchard plot failed to reveal a marked heterogeneity in the population of sites labelled with [3H]vasopressin with an affinity of 1.5 nM and a maximal binding capacity of 39 fmol/mg protein. The specificity of these binding sites, tested in competition experiments, revealed that these neurohypophyseal hormones labelled two distinct populations of sites. One population with a high affinity for vasopressin, oxytocin and vasotocin, the other population with a high affinity for vasopressin and vasotocin and a low affinity for oxytocin. Adenylate cyclase activity was not affected by arginine-vasopressin or oxytocin. These receptors are compared with previously characterized peripheral receptors.     

Two classes of receptor specific for sperm-activating peptide III in sand-dollar spermatozoa.

We characterized receptors specific for sperm-activating peptide III (SAP-III: DSDSAQNLIQ) in spermatozoa of the sand dollar, Clypeaster japonicus, using both binding and cross-linking techniques. Analyses of the data obtained from the equilibrium binding of a radiolabeled SAP-III analogueto C. japonicus spermatozoa, using Klotz, Scatchard and Hill plots, showed the presence of two classes of receptors specific for SAP-III in the spermatozoa. One of the receptors (high-affinity) had a Kd of 3.4 nM and 3.4 x 10(4) binding sites/spermatozoon. The other receptor (low-affinity) had a Kd of 48 nM, with 6.1 x 10(4) binding sites/spermatozoon. The Kd of the high-affinity receptor was comparable to the median effective concentration of the intracellular-pH-increasing activity of SAP-III and that of the low-affinity receptor was comparable to the median effective concentration of the cellular-cGMP-elevating activity of the peptide. In addition, Scatchard and Hill plots of the data suggested the existence of positive cooperativity between the high-affinity members. Similar results were also obtained from a binding experiment using a sperm-membrane fraction prepared from C. japonicus spermatozoa. The incubation of intact spermatozoa or sperm plasma membranes with the radioiodinated SAP-III analogue and a chemical cross-linking reagent, disuccinimidyl suberate, resulted in the radiolabeling of three proteins with molecular masses of 126, 87 and 64 kDa, estimated by SDS/PAGE under reducing conditions.