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Analyzing Binding Data

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Abstract
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Abstract

Measuring the rate and extent of radioligand binding provides information on the number of binding sites, and their affinity and accessibility of these binding sites for various drugs. This unit explains how to design and analyze such experiments. Curr. Protoc. Neurosci. 52:7.5.1?7.5.65. © 2010 by John Wiley & Sons, Inc.

Keywords: binding; radioligand; radioligand binding; Scatchard plot; receptor binding; competitive binding curve; IC50; Kd; Bmax; nonlinear regression; curve fitting; fluorescence

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Introduction
Binding Theory
Saturation Binding Experiments
Competitive Binding Experiments
Kinetic Binding Experiments
Two Binding Sites
Agonist Binding
Use of Fluorescence or Other Spectroscopic Methods in Binding Experiments
Basic Protocol 1: Fluorescence Saturation Binding of BODIPY FL‐GTPγS to GαO
Analyzing Data Using Nonlinear Regression
Evaluating Results of Nonlinear Regression
Comparing Treatment Groups
Calculations with Radioactivity
Analyzing Data with GraphPad Prism
Literature Cited
Figures
Tables

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Materials

Basic Protocol 1: Fluorescence Saturation Binding of BODIPY FL‐GTPγS to GαO

Materials

Ligand (BODIPY‐FL‐GTPγS; Invitrogen) stock solution: 10 µl of 100 µM frozen in 1 mM DTT
G protein (Gα_o ) stock solution: 20 µM snap frozen in HED buffer
Binding buffer: HED buffer (see below) containing 10 mM MgCl₂
HED buffer: 50 mM HEPES, pH 8, containing 1 mM EDTA and 1 mM DTT
Competing ligand (e.g., 100 µM GTPγS)

Costar 3915 black 96‐well microplate
Fluorescence plate reader

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Figures

Figure 7.5.1 Occupancy at equilibrium. The fraction of receptors occupied by a ligand at equilibrium depends on the concentration of the ligand compared to its K _d .

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Figure 7.5.2 Examples of nonspecific binding. (A ) [³ H]Mesulergine binding to serotonin receptors has low nonspecific binding (<25% of total binding at the highest concentrations). (B ) [³ H]Meproadifen binding to the ion channel of nicotinic receptors has high nonspecific binding (>50%).

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Figure 7.5.3 Total binding, specific binding, and nonspecific binding for a saturation binding experiment.

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Figure 7.5.4 Displaying results as a Scatchard plot. (A ) Specific binding as a function of free radioligand. (B ) Transformation of Scatchard data to a plot.

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Figure 7.5.5 Why Scatchard plots (though useful for displaying data) should not be used for analyzing data. (A ) Experimental data with best‐fit curve determined by nonlinear regression. (B ) Scatchard plot of the data. The solid line corresponds to the B _max and K _d determined by nonlinear regression in panel A. The dashed line was determined by linear regression of transformed data in panel B. The results of linear regression of the Scatchard plot are not the most accurate values for B _max ( x intercept) or K _d (negative reciprocal of the slope).

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Figure 7.5.6 Sample saturation binding experiment. The ligand binding to angiotensin receptors in a membrane preparation was measured. Total and nonspecific binding are shown.

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Figure 7.5.7 These data are the same as those shown in Figure . The left panel (A ) fits a curve through the specific binding data (Strategy 1). The right panel (B ) globally fits total and nonspecific binding data (Strategy 3).

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Figure 7.5.8 Scatchard transformation of the data from Figure . The solid line was created (as explained in the text) from the best‐fit values of B _max and K _d determined from nonlinear regression. This is the correct line to show on a Scatchard plot. The dashed line was determined by linear regression of the Scatchard‐transformed data. It is shown here for comparison only; it is not informative or helpful.

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Figure 7.5.9 Schematic of a competitive binding experiment.

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Figure 7.5.10 Steepness of a competitive binding curve. This graph shows the results at equilibrium when radioligand and competitor bind to the same binding site. The curve will descend from 90% binding to 10% binding over an 81‐fold increase in competitor concentration.

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Figure 7.5.11 Example of a competitive binding experiment. Yohimbine competes for radioligand binding to α₂ receptors on membranes.

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Figure 7.5.12 Example of homologous competitive binding experiment. The hot and cold ligands are identical.

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Figure 7.5.13 Examples of slope factors. The slope factor quantifies the steepness of the curve, and is determined by nonlinear regression of competitive binding data. It is not the same as the slope of the curves at the midpoints.

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Figure 7.5.14 Schematic of a dissociation kinetic experiment.

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Figure 7.5.15 Schematic of a dissociation kinetic experiment shown on a log scale. The y axis plots the natural log of specific binding.

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Figure 7.5.16 Schematic of an association kinetic experiment.

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Figure 7.5.17 Schematic of observed association rate constants as a function of radioligand concentration. Higher concentrations of radioligand equilibrate more quickly. The slope of the line equals the association rate constant ( k _on ); the y intercept is the dissociation rate constant ( k _off ).

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Figure 7.5.18 Saturation binding to two classes of receptors. The two receptor types are present in equal quantities, but have K _d values that differ by a factor of ten. (A ) Binding to the two individual receptor types are shown as dashed curves. The sum (observed experimentally) is shown as a solid curve. It is not obviously biphasic. (B ) Scatchard transformation. The curvature of the overall Scatchard plot (solid) is subtle, and it would be easy to miss the curvature if the data were scattered. Note that the Scatchard plots for the individual receptors (dashed) are not asymptotes of the two‐site Scatchard plot (solid).

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Figure 7.5.19 Two‐site competitive binding curve. The radioligand binds identically to two kinds of receptors, but these two receptors have a ten‐fold difference in affinity for the competitor. The curve is shallow, but not obviously biphasic.

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Figure 7.5.20 Discriminating between binding to two (or more) binding sites (A ) and negative cooperativity (B ). With negative cooperativity, dissociation will be faster when initiated by adding excess unlabeled ligand than when initiated by infinite dilution.

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Figure 7.5.21 The solid curve shows the fit to an equation describing competition for a single class of receptors. The dashed curve shows the fit to an equation describing competition for binding to two classes of receptors.

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Figure 7.5.22 Schematic of agonist competition for binding to a receptor linked to a G protein. In the absence of GTP (left) the curve is shallow (and in this extreme case, biphasic). In the presence of GTP (or an analog) the curve is shifted to the right and is steeper.

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Figure 7.5.23 Models for agonist binding to receptors linked to G proteins. H, hormone or agonist; R, receptor; G, G protein.

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Figure 7.5.24 Fluorescence intensity at various concentrations of receptor as a function of added ligand concentration. The upper left panel shows the total fluorescence intensity. The upper right panel converts to nM bound. The lower left panel normalizes the curve for each receptor concentration so they all plateau at the same maximum, and compares the EC₅₀ values. The lower right panel zooms in on the lowest ligand concentrations.

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Figure 7.5.25 Fluorescence saturation curves for binding of BODIPY‐FL‐GTPγS to three different G protein alpha subunits. Binding was measured as described in the with a 20 nM final concentration of Gα_o and Gα_s , incubated at room temperature for 20 min. For Gα_i1 , a final concentration of 100 nM was used with incubations for 60 min at 30°C (reprinted with permission from McEwen et al., ).

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Figure 7.5.26 Fluorescence polarization measurements of αMSH binding. Fluorescent ligand (0.5 nM BODIPY‐NDP‐αMSH) was incubated with increasing amounts of membrane containing the indicated concentrations of MC₅ receptor. Fluorescence polarization was measured and plotted versus concentration of added receptor. Data from Nosjean et al. ().

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Figure 7.5.27 Fluorescence polarization measurements of αMSH binding with varying ligand. Membranes containing 1 nM MC₅ receptor were incubated with increasing amounts of fluorescent ligand (BODIPY‐NDP‐αMSH). Fluorescence polarization was measured and plotted versus concentration of added ligand. As indicated in the text, the fraction of bound ligand (and the polarization) is highest at the low ligand concentrations. These data were fitted using NLLSQ analysis with Equation , with a fixed value of R _T = 1.0 nM (Nosjean et al., ). Although the concentration of ligand at which the polarization falls to a half‐maximal value is about 2 nM, the calculated K _d is 0.43 nM due to ligand depletion that occurs because R _T > K _d .

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Figure 7.5.28 A dose‐response curve with data collected over a narrow range of concentrations. When a nonlinear regression program tries to fit the top and bottom plateaus as well as the EC₅₀ and slope, the resulting confidence intervals are very wide. Since there is no data to define zero and one hundred, the program will be very uncertain about the EC₅₀ . If the nonlinear regression program is told to set the top and bottom plateaus to constant values (from controls), then it can determine the EC₅₀ with precision.

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Figure 7.5.29 A dose response curve with no data in the middle of the curve. Since there are no data points in the middle of the curve, the best‐fit value of the EC₅₀ will be uncertain with a wide confidence interval.

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Figure 7.5.30 Residuals. The top panel (A ) graphs dissociation kinetic data. The bottom panel (B ) shows the residuals (i.e., the y axis plots the distance between the point and the curve from the top panel).

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Figure 7.5.31 What is a false minimum? A nonlinear regression program stops when making any small change to a parameter will worsen the fit and thus raise the sum of squares. In rare cases, this may happen at a false minimum rather than the true best fit value.

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Figure 7.5.32 Counting error. With more counts, the fractional counting error decreases. The x axis shows the number of radioactive decays actually counted (counts per minute times number of minutes).

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Analyzing Binding Data

Abstract

Table of Contents

Materials

Basic Protocol 1: Fluorescence Saturation Binding of BODIPY FL‐GTPγS to GαO

Figures

Videos

Literature Cited