What is a Scatchard plot?

In this plot, the X-axis is specific binding and the Y-axis is specific binding divided by free radioligand concentration. It is possible to estimate the Bmax and Kd from a Scatchard plot (Bmax is the X intercept; Kd is the negative reciprocal of the slope). However, the Scatchard transformation distorts the experimental error, and thus violates several assumptions of linear regression. The Bmax and Kd values you determine by linear regression of Scatchard transformed data may be far from their true values.

Tip. You should analyze saturation binding data with nonlinear regression not with Scatchard plots. Use Scatchard plots to display data, not to analyze data.

After analyzing your data with nonlinear regression, however, it is often useful to display data as a Scatchard plot. The human retina and visual cortex are wired to detect edges (straight lines), not rectangular hyperbolas. Scatchard plots are often shown as insets to the saturation binding curves. They are especially useful when you want to show a change in Bmax or Kd.

When making a Scatchard plot, you have to choose what units you want to use for the Y-axis. Some investigators express both free ligand and specific binding in cpm so the ratio bound/free is a unitless fraction. While this is easy to interpret (it is the fraction of radioligand bound to receptors), a more rigorous alternative is to express specific binding in sites/cell or fmol/mg protein, and to express the free radioligand concentration in nM. While this makes the Y-axis hard to interpret visually, it provides correct units for the slope (which equals -1/KD).  

Transforming data to create a Scatchard plot

Prism cannot plot a Scatchard plot automatically, but it is very easy to transform the data to create a Scatchard plot. Use the same instructions for one- and two-site binding.

To transform specific binding data to a Scatchard plot:

1. Start from a table where X is concentration of ligand in nM or pM and Y is specific binding. This can either be the original data table or a results table.

2. Press Analyze and choose built-in analyses.

3. From the data manipulation section, choose Transforms.

4. If your table has more than one data set, choose to analyze selected data sets only and choose one data set. The Scatchard transform can only be used with one data set at a time.

5. Check the box to interchange X and Y.

6. Check the box to transform Y and choose the Y transform: Y=X/Y.

7. Check the box to make a new graph.If you do Scatchard transforms frequently, save these steps into a method or template.   

Plotting the line that corresponds to nonlinear regression analyses

If there is one class of receptors, the Scatchard plot will be linear. Some people use linear regression to draw a line through the points. To do this, start from either the graph or a table of the Scatchard transformed data. Click the analyze button and choose linear regression. You may need to change the limits of the regression line to create an attractive graph.

The linear regression line should NOT be used to analyze the data. The X-intercept of the regression line will be near the Bmax and the negative inverse of the slope will be near the Kd. However, the Bmax  and Kd  values determined directly with nonlinear regression will be more accurate.

It isn't hard to draw the Scatchard line that corresponds to the nonlinear regression determination of Bmax  and Kd. The discussion below assumes that the "bound" units for the Y axis are the same units used for the X-axis and in which you want to express Bmax (sites/cell or fmol/mg,), and the "free" units are the same as the units you want to use for the Kd  (nM or pM). Since the X intercept of the Scatchard line is the Bmax, the Scatchard line ends at X=Bmax, Y=0. Since the slope of the Scatchard line equals -1/Kd , the Y-intercept equals the Bmax   divided by the Kd. So the Scatchard line begins at X=0, Y=Bmax/Kd.

To create a Scatchard line corresponding to the nonlinear regression fit:

1. Create a new data table, with numerical X values and single Y values.

2. Into row 1 enter X=Bmax (previously determined by nonlinear regression), Y=0.

3. Into row 2 enter X=0, Y=Bmax/Kd  (computed manually from the results of nonlinear regression).

4. Note the name of this data table. Perhaps rename to something appropriate.

5. Go to the Scatchard graph.

6. Press Change, then Data on graph.

7. Add the new data table to the graph.

8. Press Change, then Symbols and lines.

9. Drop down the list of data sets, and select the one you noted in step 4.

10. Choose to plot no symbols, but to connect with a line.

Scatchard plots of binding to two sites

The appearance of a two-site Scatchard plot.

The left panel below shows binding of a radioligand to two independent binding sites present in equal concentrations, but with a tenfold difference in Kd . The two individual curves are shown as dotted and dashed curves. When you do the experiment, you can't observe the individual components, but observe the sum, which is shown as a solid curve. Note that this curve is not obviously biphasic.

The right panel shows the same data plotted on a Scatchard plot. The binding to each receptor is shows as a straight line (dotted, or dashed). The total binding, plotted on a Scatchard plot, is curved. Note that the two lines that represent binding to each type of receptor are NOT the asymptotes of the curve.

Graphing data on a two-site Scatchard plot

See Transforming data to create a Scatchard plot. You don't need to do anything differently when there are two kinds of receptors.

Graphing the two lines of a two-site Scatchard plot.

To plot the two straight lines that correspond to the nonlinear regression fit, adapt the instructions for plotting a Scatchard plot for one-site binding. See Plotting the line that corresponds to nonlinear regression analyses. Create a new data table that defines the two lines as shown below, using Bmax  and Kd values determined by nonlinear regression.

X	A	B
0	Bmax1/Kd1
Bmax1	0
0		Bmax2/Kd2
Bmax2		0

Go to the graph of the Scatchard transformed data and add the new table to that graph. Use the Symbols dialog to plot the two data sets from the table using connecting lines but no symbols.

Graphing the curve on a two-site Scatchard plot.

If the radioligand binds to two binding sites, the Scatchard plot will be curved but you cannot create the curve using nonlinear regression. This approach is not appropriate, because the specific binding data appear on the X-axis and as part of the Y-axis, and this violates a major assumption of nonlinear regression.

You should determine Kd  and Bmax   of both receptor types using nonlinear regression to fit the specific binding data. See Determining Kd and Bmax for two classes of binding sites. The resulting curve is defined by a number of line segments. To graph the best-fit curve on a Scatchard plot, transform each point that defines the best-fit curve to Scatchard axes, and connect the points. With GraphPad Prism, follow these steps:

1. Use nonlinear regression to fit the specific binding data to a two-site binding curve. While on the nonlinear regression parameters dialog, click the Output options button and check the option box to view the table of XY coordinates defining the curve.

2. Go to the nonlinear regression results. Drop the view list and select Curve.

3. Click Analyze, and choose Transform from the list of data manipulations.

4. To do a Scatchard transformation, check the option box to interchange X and Y values. Also check the box to transform Y and choose the Y transform: Y=X/Y. Do not check the box to make a new graph. The results will be the best-fit curve transformed to fit Scatchard axes.

5. Make a note of the name of the sheet with the Scatchard transformed curve data. Consider renaming the sheet.

6. Go to the graph of the Scatchard transformed data.

7. Click Change and choose Data on graph.

8. Add the data set that contains the Scatchard transformation of the best-fit curve (created in step 4).

9. Click Change and choose Symbols and lines.

10. Drop the list of data sets, and choose the Scatchard transformation of the best-fit curve.

11. Choose to plot no symbols, but to connect with a line.