Saturation Binding Curves and Scatchard Plots

In this step-by-step example, we'll make a commonly used combination graph — saturation binding curve with an inset Scatchard plot.

Scatchard analysis is a method of linearizing data from a saturation binding experiment in order to determine binding constants. One creates a "secondary" plot of specific binding/free radioligand concentration (Y axis) vs. specific binding (X axis). 

Now that programs such as Prism easily do nonlinear regression, the best way to determine Kd and Bmax is to fit a hyperbola directly to the saturation isotherm. Yet Scatchard analysis remains a good way to visualize saturation binding data. We'll show how to combine these techniques, creating a conventional Scatchard plot, but superimposing a line that reflects the best possible estimates of Kd and Bmax.

Create a Table of Specific Binding Data

When you launch Prism, the Welcome to GraphPad Prism dialog appears. It lets you create a new project (file) or open an existing one. Choose to Create an XY data table. The lower portion of the Welcome dialog presents choices for formatting the first data table. For the X values, select Numbers. For the Y columns, choose the format that fits your data; to keep data entry in this example short, we'll use enter and plot a single Y value for each point. When you click OK, Prism displays the new table.

For each point on the saturation binding curve, enter the concentration of ligand into the X column and the value for specific binding into the Y column. The units you use are up to you — use whatever is meaningful. Just remember that Prism will graph the data and compute the binding parameters in whatever units you've used on your table. Place labels over the X and Y columns as a reminder.

Here are the data for our example:

Click on the Graphs section of the Navigator (left) panel, to view the graph of your data.

Fit the Saturation Binding Curve to Compute Kd and Bmax

Click on the Analyze button. From the XY analyses category, select Nonlinear regression (curve fit). Click OK.

In the Parameters: Nonlinear regression dialog box, choose Classic equations. Select One site binding (hyperbola).

The units for Bmax are the units that you used when entering Y values on the original data table. The units for Kd are the units you used when entering the X values.

Display Binding Constants on the Graph

If you wish, you can paste cells from this results table to your graph, so that your binding constants will be displayed there and will also be linked to the results sheet. That way, if you change the saturation binding data later, Bmax and Kd will be automatically updated both on the results sheet and on the graph. If you don't like the way the pasted data are displayed, you can change that. Select a cell on the results sheet containing the value you want to paste. Choose Edit... Copy.

Switch to the graph, and choose Edit... Paste Table. The value is placed on the graph, and you can drag it wherever you want. Double-click on the embedded table to bring up formatting options. Here is a finished example:

At this point, you may wish to change some of your original saturation binding data (data table) and observe how the values of Bmax and Kd change automatically on the results sheet and on the graph.

Prepare the Scatchard Transforms

We'll start the Scatchard analysis by transforming the saturation binding data. The original data table has the "free" ligand concentration in the X column and the "bound" ligand concentration in the Y column. To get "bound" in the X column and "bound/free" in the Y column, we need to do some transforming. From the original table containing the saturation binding data, click Analyze and select Transform, Normalize... and Transform.

In the next dialog, Parameters: Transform, choose to interchange X and Y and then to replace Y with X/Y. Here are the settings for the transforms:

The transformed data are shown on a new results sheet (the original data are unchanged in the "Data tables" section of your project). Prism will carry over the original column titles, which will now be incorrect, so you can edit them:

Complete the Scatchard Plot

The default Scatchard plot appears as the most recently generated graph. You will notice that there is no line superimposed over the points. We recommend that you add a line to your graph that connects the X and Y axis intercepts in such a way as to accurately reflect the Kd and Bmax values that we have just found by nonlinear regression. Referring to the results sheet for your nonlinear regression analysis, compute the Y coordinate for the Y axis intercept manually as

Bmax/Kd = 545.5/24.43 = 22.33

Switch to the table section of your project, choose New Table, and select an XY data table. Fill in the table using the values for Bmax and Bmax/Kd as follows:

1. Into row 1 enter X = 0, Y = Bmax/Kd
2. Into row 2 enter X = Bmax, Y = 0

Here's the table:

Note the name of this data table. You may wish to rename it to something more meaningful, such as "Scatchard Line Data". Now switch to the Scatchard plot, i.e., the graph we created in the previous section. Double-click on the graph to bring up the Format Graph dialog. Switch to the Data Sets on Graph tab and select Add. Add the Scatchard Line Data to your graph. 

This results in the Y and X intercepts being plotted as points. Format this data set to make the points invisible but to connect them with a line: Double-click on the graph to bring up the Format Graph dialog, and adjust the following settings:

Here is the Scatchard plot, with a few a formatting changes that we haven't covered here:

Create a Layout Showing the Saturation Isotherm, with Inset Scatchard Plot

Switch to the Layout section of your project, and click New Layout. Choose the Landscape orientation and the Inset arrangement:

When you click OK, you'll see a layout with two placeholders. Double-click on each in turn, assigning your saturation binding plot to the larger, and your Scatchard plot to the smaller, placeholder. Alternatively, you can drag and drop each plot into the appropriate location. Then move and resize the Scatchard plot. Here is your resulting graph:

Important note: If, after viewing your layout, you want to resize individual objects/labels to enhance readability, switch back to the appropriate graph sheet and make the changes there. Test the changes by switching back to the layout, which updates automatically. One exception to this is when you want to change the size of the overall layout or change the sizes of the two graphs on the layout relative to one another. Do that directly on the layout, by selecting the inset graph, or the entire layout, and then dragging as appropriate.