Competitive binding experiments measure the binding of a single concentration of labeled ligand in the presence of various concentrations of unlabeled ligand. Ideally, the concentration of unlabeled ligand varies over at least six orders of magnitude.

The top of the curve is a plateau at a value equal to radioligand binding in the absence of the competing unlabeled drug. The bottom of the curve is a plateau equal to nonspecific binding. The concentration of unlabeled drug that produces radioligand binding half way between the upper and lower plateaus is called the IC50 (inhibitory concentration 50%) or EC50 (effective concentration 50%).

If the radioligand and competitor both bind reversibly to the same binding site, binding at equilibrium follows this equation (where Top and Bottom are the Y values at the top and bottom plateau of the curve).

Entering data for competitive binding curves

Most investigators enter Y values as cpm. If you performed the experiment in triplicate, enter all three values and let Prism automatically plot the error bars.

Some investigators transform their data to percent specific binding. The problem with this approach is that you need to define how many cpm equal 100% binding and how many equal 0% specific binding. Deciding on these values is usually somewhat arbitrary. It is usually better to enter the data as cpm.

Enter the logarithm of the concentration of competitor into the X column. For example, if the competitor concentration varied from 1 nM to 1 mM, enter X values from -9 to -3. A log axis cannot accommodate a concentration of zero (log(0) is undefined). Instead, enter a very low competitor concentration (in this example, 10).

If you prefer to enter concentrations in the data table, rather than the logarithm of concentration, transform the data before performing nonlinear regression. Follow these steps:

1. Enter the data with X as concentration of ligand and Y as binding.

2. Press Analyze.

3. From the data manipulation section, choose Transforms.

4. Check Transform X values.

5. Choose X=log(X).

6. If you want to transform Y from cpm to more useful units, check Transform Y values, choose Y=K*Y, and enter an appropriate value for K.

7. Check the option box to make a new graph of the transformed data.Note: When fitting a curve with nonlinear regression, be sure to fit to the new transformed data table or the new graph.

Decisions to make before fitting the data

Weighting

When analyzing the data, you need to decide whether to minimize the sum of the squares of the absolute distances of the points from the curve or to minimize the sum of the squares of the relative distances. The choice depends on the source of the experimental error. Follow these guidelines:

	•	If the bulk of the error comes from pipetting, the standard deviation of replicate measurements will be, on average, a constant fraction of the amount of binding. In a typical experiment, for example, the highest amount of binding might be 2000 cpm with an SD of 100 cpm. The lowest binding might be 400 cpm with an SD of 20 cpm. With data like this, you should evaluate goodness-of-fit with relative distances. The details on how to do this are in the next section.

	•	In other experiments, there are many contributions to the scatter and the standard deviation is not related to the amount of binding. With this kind of data, you should evaluate goodness-of-fit using absolute distances, which is the default choice.

	•	You should only consider weighting by relative distances when you are analyzing total binding data. When analyzing specific binding (or data normalized to percent inhibition), you should evaluate goodness-of-fit using absolute distances, as there is no clear relationship between the amount of scatter and the amount of specific binding.

Constants

To find the EC50, the concentration that blocks 50% of the binding, Prism needs to first define 100% and 0%.

Ideally your data span a wide range of concentrations of unlabeled drug, and clearly define the bottom or top plateaus of the curve. If this is the case, Prism can fit the 0% and 100% values from the plateaus of the curve and you don't need to do anything special.

In some cases, your competition data may not define a clear bottom plateau, but you can define the plateau from other data. All drugs that bind to the same receptor should compete all specific radioligand binding and reach the same bottom plateau value. This means that you can define the 0% value (the bottom plateau of the curve) by measuring radioligand binding in the presence of a standard drug known to block all specific binding. If you do this, make sure that you use plenty of replicates to determine this value accurately. If your definition of the lower plateau is wrong, the values for the IC50 will be wrong as well. You can also define the top plateau as binding in the absence of any competitor.

If you have collected enough data to clearly define the entire curve, let Prism fit all the variables and fit the top and bottom plateaus based on the overall shape of your data. If your data don't define a clear top or bottom plateau, you should define one or both of these values to be constants fixed to values determined from other data.