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Analyzing Radioligand Binding Data
Publication Name:
Current Protocols in Protein Science
Unit Number:
Appendix 3H
DOI:
10.1002/0471140864.psa03hs21
Online Posting Date:
May, 2001 Abstract
A radioligand is a radioactively labeled drug that can associate with a receptor, transporter, enzyme, or any protein of interest. Measuring the rate and extent of binding provides information on the number of binding sites, and their affinity and accessibility for various drugs. Radioligand binding experiments are easy to perform, and provide useful data in many fields. For example, radioligand binding studies are used to study receptor regulation, investigate receptor localization in different organs or regions using autoradiography, categorize receptor subtypes, and probe mechanisms of receptor signaling. This unit reviews the theory of receptor binding and explains how to analyze experimental data. Since binding data are usually best analyzed using nonlinear regression, this unit also explains the principles of curve fitting with nonlinear regression.
Table of Contents
- Unit Introduction
- Binding Theory
- Saturation Binding Experiments
- Competitive Binding Experiments
- Kinetic Binding Experiments
- Two Binding Sites
- Agonist Binding
- 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
Figures
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Figure A.3H.1Occupancy at equilibrium. The fraction of receptors occupied by a ligand at equilibrium depends on the concentration of the ligand compared to its Kd . -
Figure A.3H.2Examples 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%). -
Figure A.3H.3Total binding, specific binding, and nonspecific binding for a saturation binding experiment. -
Figure A.3H.4Displaying results as a Scatchard plot. (A) Specific binding as a function of free radioligand. (B) Transformation of Scatchard data to a plot. -
Figure A.3H.5Why 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 Bmax and Kd 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 forBmax (x intercept) orKd (negative reciprocal of the slope). -
Figure A.3H.6Sample saturation binding experiment. The ligand binding to angiotensin receptors in a membrane preparation was measured. Total and nonspecific binding are shown. -
Figure A.3H.7Specific binding with the best-fit curve determined by nonlinear regression. These data are the same as those shown in Figure -
Figure A.3H.8Scatchard transformation of the data from Figuremax andKd 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. -
Figure A.3H.9Schematic of a competitive binding experiment. -
Figure A.3H.10Steepness 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. -
Figure A.3H.11Example of a competitive binding experiment. Yohimbine competes for radioligand binding to2 receptors on membranes. -
Figure A.3H.12Example of homologous competitive binding experiment. The hot and cold ligands are identical. -
Figure A.3H.13Examples 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. -
Figure A.3H.14Schematic of a dissociation kinetic experiment. -
Figure A.3H.15Schematic of an association kinetic experiment. -
Figure A.3H.16Schematic of a dissociation kinetic experiment shown on a log scale. They axis plots the natural log of specific binding. -
Figure A.3H.17Schematic 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 (kon ); the y intercept is the dissociation rate constant (koff ). -
Figure A.3H.18Saturation binding to two classes of receptors. The two receptor types are present in equal quantities, but haveKd 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) arenot asymptotes of the two-site Scatchard plot (solid). -
Figure A.3H.19Two site competitive binding curve. The radioligand binds identically to two kinds of receptors, but these two receptors have a tenfold difference in affinity for the competitor. The curve is shallow, but not obviously biphasic. -
Figure A.3H.20Discriminating between binding to two (or more) binding sites (top) and negative cooperativity. With negative cooperativity, dissociation will be faster when initiated by adding excess unlabeled ligand than when initiated by infinite dilution. -
Figure A.3H.21The 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. -
Figure A.3H.22Schematic 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. -
Figure A.3H.23Models for agonist binding to receptors linked to G proteins. H, hormone or agonist; R, receptor; G, G protein. -
Figure A.3H.24Residuals. The top panel graphs dissociation kinetic data. The bottom panel shows the residuals (i.e., they axis plots the distance between the point and the curve from the top panel). -
Figure A.3H.25A 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. -
Figure A.3H.26A 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. -
Figure A.3H.27What is a false minimum? A nonlinear regression program stops when making any small change to a variable 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. -
Figure A.3H.28Counting error. With more counts, the fractional counting error decreases. Thex axis shows the number of radioactive decays actually counted (counts per minute times number of minutes).
Literature Cited
| Literature Cited | |
| Cheng, Y. and Prusoff, W.H. 1973. Relationship between the inhibition constant (K | |
| Kenakin, T. 1993. Pharmacologic Analysis of Drug-Receptor Interactions. Raven Press, New York. | |
| Limbird, L.E. 1996. Cell Surface Receptors: A Short Course in Theory and Methods, 2nd ed. Kluwer Academic Publishers, Boston. | |
| Motulsky, H.J. and Mahan, L.C. 1984. The kinetics of competitive radioligand binding predicted by the law of mass action. Mol. Pharmacol. 25:1-9. | |
| Munson, P.J. and Rodbard, D. 1980. Ligand: A versatile computerized approach to characterization of ligand binding systems. Anal. Biochem. 107:220-239. | |
| Rosenthal, H.E. 1967. A graphic method for the determination and presentation of binding parameters in complex systems. Anal. Biochem. 20:525-532. | |
| Swillens, S. 1995. Interpretation of binding curves obtained with high receptor concentrations: Practical aid for computer analysis. Mol. Pharmacol. 47:1197-1203. | |
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