Model Testing in Radioligand/Receptor Interaction by Monte Carlo Simulation

Abstract

Monte Carlo simulations have been applied for evaluating the reliability of parameter estimates as well as for testing models in radioligand saturation binding experiments. Scatchard analysis was compared to the nonlinear least-square curve fitting method for one-site saturation binding curves. It was found that linear regression analysis from the transformed data in the Scatchard plot yielded generally less accurate parameter estimates than nonlinear regression analysis of untransformed data. The advantage of the nonlinear least-squares curve fitting method was especially pronounced in cases where the scatter and number of data points, as well as the radioligand concentration range, were chosen similar to less optimal experimental conditions. Under such circumstances, several K_D and B_max values derived by Scatchard analysis led to physically impossible negative values whereas the same data analyzed by nonlinear regression yielded reasonable parameter estimates. Furthermore, it was found that for both means of analysis, K_D and B_max correlated positively. In another set of Monte Carlo experiments, saturation binding curves involving two receptor sites were generated and subsequently analyzed according to both a one-site and a two-site model. The confidence with which one is able to distinguish the two-site model from nonlinear least-squares curve fitting was then estimated for optimal, as well as for, less ideal experimental condigions.     

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.     

The binding of Ca2+ to Ca2+-transporting microsomes derived from bovine uterine sarcoplasmic reticulum

An obligatory early step in the transport of calcium across the internal membranes of smooth muscle cells is the binding of calcium to the Ca,Mg-ATPase. The characterization of calcium binding to sarcoplasmic reticulum from smooth muscle has not been reported. Calcium binding to a bovine myometrium preparation was investigated using Scatchard analysis and a computer program utilizing weighted least squares curve fitting and an exact mathematical model of binding. This permitted objective measurement of goodness of fit and showed that best fit was obtained using a two site model. Magnesium did not change the affinity for calcium of the two sites; but reduced the number of low affinity sites to half.     

Negatively cooperative binding of high-density lipoprotein to the HDL receptor SR-BI

Scavenger receptor class B, type I (SR-BI), is a high-density lipoprotein (HDL) receptor, which also binds low-density lipoprotein (LDL), and mediates the cellular selective uptake of cholesteryl esters from lipoproteins. SR-BI also is a coreceptor for hepatitis C virus and a signaling receptor that regulates cell metabolism. Many investigators have reported that lipoproteins bind to SR-BI via a single class of independent (not interacting), high-affinity binding sites (one site model). We have reinvestigated the ligand concentration dependence of (125)I-HDL binding to SR-BI and SR-BI-mediated specific uptake of [(3)H]CE from [(3)H]CE-HDL using an expanded range of ligand concentrations (<1 μg of protein/mL, lower than previously reported). Scatchard and nonlinear least-squares model fitting analyses of the binding and uptake data were both inconsistent with a single class of independent binding sites binding univalent lipoprotein ligands. The data are best fit by models in which SR-BI has either two independent classes of binding sites or one class of sites exhibiting negative cooperativity due to either classic allostery or ensemble effects ("lattice model"). Similar results were observed for LDL. Application of the "infinite dilution" dissociation rate method established that the binding of (125)I-HDL to SR-BI at 4 °C exhibits negative cooperativity. The unexpected complexity of the interactions of lipoproteins with SR-BI should be taken into account when interpreting the results of experiments that explore the mechanism(s) by which SR-BI mediates ligand binding, lipid transport, and cell signaling.     

Nitrobenzylthioinosine binding cooperativity in chromaffin tissue membranes.

The nucleoside transporter present in chromaffin tissue membranes has been studied by [3H]nitrobenzylthioinosine (NBTI) binding. This ligand presents a high affinity, with a Kd value of 2.1 +/- 0.2 nM and a Bmax of 1.7 +/- 0.2 pmol/mg protein. From the Scatchard and the semilogarithmic graphical representations a positive cooperativity was deduced, with a Hill coefficient of 1.7 +/- 0.4. In displacement studies of NBTI by the non labelled compound, the Hill coefficient was also higher than 1 (1.44 +/- 0.11) in the presence of ATP. This nucleotide seems necessary to maintain the number of high affinity binding sites.     

Altered estrogen receptor system in estrogen-unresponsive human endometrial adenocarcinoma cells

Previous studies from our laboratories demonstrated that cells from a human endometrial adenocarcinoma cell line (Ishikawa) responded to estradiol whereas cells from another endometrial cancer line (HEC-50) did not. In an attempt to identify factors responsible for the observed estrogen insensitivity we compared the characteristics of the estradiol receptor (ER) systems in Ishikawa and HEC-50 cells. Saturation analyses of cytosolic estrogen binders were performed over a 0.1-70 nM range of [3H]estradiol concentrations. Equilibrium dissociation constants and number of binding sites were determined by graphic analysis of Scatchard plots or computed by applying Fourier-derived affinity spectrum analysis (FASA) of the binding data. No significant differences were noted in the dissociation constants (Kd approx. 0.6 nM) or number of binding sites (approx. 6-10 fmol/mg protein) for the single binder that could be evaluated by the graphic method in cytosol from the two cell lines. However, 2 binders in Ishikawa cells (Kd approx. 0.2 and 6 nM) could be detected by the FASA method; the higher affinity binder in HEC-50 cells could not be clearly demonstrated. Structural differences in the specific estrogen binders which might distinguish HEC-50 from Ishikawa cells or normal endometrial tissue were investigated by using the anti-ER monoclonal antibody JS 34/32. Interaction of the antibody with [3H]estradiol binders of estrogen-responsive cells and tissue was evident from the formation of labeled complexes that were shown to sediment faster in glycerol density gradients and could be immunoprecipitated with Protein A attached to Sepharose beads. In contrast, the antibody did not recognize labeled specific binders in the HEC-50 cells. Furthermore, [3H]estradiol receptors in Ishikawa cells could be transformed into a species that exhibited increased hydrophilicity, evident from its binding to DNA-cellulose, whereas binders from HEC-50 could not. These results indicate that the lack of responsiveness of HEC-50 cells to estrogens might be due to structural or functional alterations in the ER protein resulting in a loss of its capability to undergo estrogen-directed conformational changes required for biological activity.     

Discrimination of Multiple [3H]5-Hydroxytryptamine Binding Sites by the Neuroleptic Spiperone in Rat Brain

Certain neuroleptic drugs, such as spiperone and (+) butaclamol, can discriminate between two populations of [³H]5-hydroxytryptamine ([³H]5-HT) binding sites in rat brain. The butyrophenone neuroleptic spiperone shows the greatest selectivity for these two binding sites, having at least a 3000-fold difference between its dissociation constants (2-12 nM versus 35,000 nM) for the high- and low-affinity sites, respectively. Inhibition of [³H]5-HT binding by spiperone in rat frontal cortex and corpus striatum yields distinctly biphasic inhibition curves with Hill slopes significantly less than unity. Results from nonlinear regression analysis of these inhibition studies were consistent with a two-site model in each brain region. In the frontal cortex the high-affinity neuroleptic sites comprised about 60% of the total [^3/H]5-HT binding sites whereas in the corpus striatum they accounted for only 20% of the sites. Furthermore, saturation studies of [³H]5-HT binding assayed in the absence or presence of 1 μM-spiperone (a concentration that completely blocks the high-affinity site while having minimal activity at the low-affinity site) reveal a parallel shift in the Scatchard plot with no change in the dissociation constant of [³H]5-HT, but a significant decrease (64% in frontal cortex or 28% in corpus striatum) in the number of specific binding sites. These observations are consistent with the existence of at least two populations of [³H]5-HT binding sites having a differential regional distribution in rat brain.     

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.     

Evidence for Distinct 5-Hydroxytryptamine2 Binding Site Subtypes in Cortical Membrane Preparations

5-Hydroxytryptamine (5-HT) displays a sixfold higher affinity for 5-HT2 binding sites labeled by [3H]ketanserin in rat (IC50 = 200 +/- 40 nM) and human (IC50 = 190 +/- 50 nM) cortex than for 5-HT2 sites in bovine cortex (IC50 = 1,200 +/- 130 nM). The Hill slopes of the 5-HT competition curves are 0.67 +/- 0.04 in rat, 0.69 +/- 0.08 in human, and 0.96 +/- 0.02 in bovine cortex. Scatchard analysis of (+/-)-[3H]4-bromo-2,5-dimethoxyamphetamine ([3H]DOB) binding in the rat indicates a population of binding sites with a KD of 0.38 +/- 0.04 nM and a Bmax of 1.5 +/- 0.05 pmol/g tissue. In contrast, specific [3H]DOB binding cannot be detected in bovine cortical membranes. These data indicate that species variations exist in 5-HT2 binding site subtypes and that [3H]ketanserin appears to label a homogeneous population of 5-HT2 binding site subtypes in bovine cortex.     

Determination of binding parameters in the presence of coupled reactions

Components of a binding reaction may undergo nonbinding reactions: receptors may be degraded, internalized, or exchanged with cryptic sites; ligand may be degraded or compartmented. In such cases the parameters that characterize the system are not obtained from the usual equilibrium analyses. We have simulated the reactions of such systems and generated association curves, "Scatchard" plots, and "Scatchard-like" plots that permit the calculation of binding affinity and receptor number not normally calculable under nonequilibrium binding conditions. In particular, we show that certain coupled reactions produce local maxima and sigmoid shapes in association curves and that the maxima can be used to obtain affinities and receptor numbers.     

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.     

Avermectin B1a Modulation of γ-Aminobutyric Acid Receptors in Rat Brain Membranes

Avermectin B1a stimulates high-affinity binding of [3H]-gamma-aminobutyric acid (GABA) to receptors in washed rat brain membranes. Scatchard analysis of the data indicates that the drug does not significantly alter the apparent dissociation constant of GABA binding, but increases the detectable number of binding sites from 3.2 to 5.1 pmol/mg protein, (+)-Bicuculline completely blocks control and avermectin B1a-stimulated GABA binding, whereas picrotoxin antagonizes specifically the avermectin B1a-stimulated GABA binding. The avermectin B1a-stimulated GABA binding is also chloride ion-dependent, whereas GABA binding in the control is not. These observations suggest that the mechanism of avermectin B1a stimulation of GABA binding may involve the chloride ion channel.     

92 Novel interpretation of the isotherms of multimodal ligands binding with DNA

The binding of ligands with DNA is a key moment in a whole range of cellular processes that provide not only the normal cell vital activity but also the development of some pathological processes. Depending on ligand type, structure of DNA adsorption centers, and physical–chemical conditions of the surrounding, the ligand may bind to DNA by several modes [1]. Particularly, adsorption isotherm of multimodal ligands binding to DNA in Scatchard’s coordinates has a concave shape with two brightly expressed linear areas in the region of small fillings. The analysis of such type of adsorption isotherm for determining of important binding parameters such as binding constant and number of adsorption centers (the part of DNA polymer with which one ligand molecule binds) presents difficulties. Practically in all cases, the analysis of such adsorption isotherm is carried out by linear parts of curves. Such analysis mode of experimental points is approximate method, since all registered of experimental points are roughly divided into two groups and they are treated by linear binding isotherm and therefore the binding parameters are determined. In the present work, the non-linear adsorption isotherm in Scatchard‘s coordinates is obtained which allowed, provided, the more precise treatment of all experimental points by unique curve which includes linear regions as well. Such mode of treatment of experimental points makes more precise the determination of not only binding constant and number of adsorption centers that correspond to the one ligand molecule binding, but also additional binding parameter – a proportion of adsorption centers of each binding to DNA type of multimodal ligand.     

High- and Low-Affinity Binding Components for [3H]Imipramine in Rat Cerebral Cortex

The present study demonstrates that [3H]imipramine binds to both high- and low-affinity imipramine binding components on membranes prepared from rat cerebral cortex. Scatchard and computer analyses of saturation experiments using a wide range of [3H]imipramine concentrations (0.5 nM-50 nM) revealed the presence of two binding components. Inhibition experiments in which membranes were incubated with [3H]imipramine and various concentrations of unlabelled imipramine gave shallow inhibition curves with a Hill coefficient of 0.60 +/- 0.04. When dissociation rates of imipramine were studied, biphasic dissociation curves were obtained with apparent half-times of dissociation of 2.5 +/- 0.4 min and 18.5 +/- 2.5 min. Thus analysis of saturation, competition, and dissociation experiments indicate that [3H]imipramine binds to low as well as high-affinity binding sites in rat cortex.     

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.     

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.     

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.     

A simplified method to determine binding parameters in a two-site case using linear regression

A program using a simplified method to compute estimates of binding parameters in a system with two independent classes of binding sites is presented. An iterative method is used to approximate step-by-step the two lines describing the binding activities separately, starting from a curvilinear Scatchard or Hofstee plot. This method is designed for use on microcomputers with graphic facilities and on programmable hand-held calculators.     

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.