One-Site Versus Two-Site Competition Experiments

Two site binding is likely to occur in a competition experiment under the following conditions:

• If the unlabeled ligand is an agonist. Receptors have both low and high affinity states for agonist. Unless steps are taken to convert all the receptor molecules into either high or low affinity states, agonist will bind to more than one affinity state of a receptor in a competition experiment.
• If the unlabeled ligand binds to different subtypes of the receptor with different affinities and there is more than one subtype in the tissue you are studying.
• If the unlabeled ligand binds to more than one receptor with different affinities. This assumes the radioligand is also binding to more than one receptor.

The characteristics of a competition curve with one-site binding are a sigmoid curve with:

• a slope of 1.0.
• there is a 81 fold difference in the concentration between 90% specific bound and 10% specific bound.

The characteristics of a competition curve with two-site binding is a sigmoid curve with

• a slope less than 1.0 (graph below on left)
• or evidence of two slopes separated by a plateau. (graph below on right)

There are two ways of doing nonlinear regression analyzing a two-site competition curve:

• Fit the data to the equation for two binding sites competition curve

Where Span = Top - Bottom of curve
X = Log Concentration of unlabeled drug
Y = Amount of Radiolabeled ligand bound
Fraction1 = Fraction of total binding that is Site 1
1-Fraction1 = Fraction of total binding that is Site 2
Log IC50₁ and Log IC50₂ are the IC₅₀ values for site one and two.

This equation assumes that both binding sites have an equal affinity for radioligand.

This equation will allow you to determine the Log IC₅₀ for the two sites as well as the % of the binding sties that have the log affinity and high affinity for the unlabeled ligand.

• Fit the data to a sigmoid curve

Where X = log of concentration of unlabeled drug
Y = Amount of radiolabeled drug bound
Top = top of the curve
Bottom = bottom of the curve
Hill slope is the slope of the curve

This equation gives one IC₅₀ value and the slope of the line (Hill slope).   As indicated above the slope of the line will be close to one if the data best fits a one-site model and less than 1 if the data best fits a two site model.

The Bylund plot is a plot of Bound vs. Bound X Inhibitor concentration using the equation (Analytical Biochem. 159:50-57, 1986)

Where B¹ = binding to site1
B² = binding to site 2
I = concentration of inhibitor
IC₅₀¹ = IC₅₀ for site 1
IC₅₀² = IC₅₀ for site 2
B_o¹ = binding to site 1 in the absence of inhibitor
B_o² = binding to site 2 in the absence of inhibitor

The graph from a sample two-site fit are shown below. The dashed blue lines indicate the individual fits for the two sites.

Notice how the graph is curved for a two site fit, but linear for a one-site fit. Like the Rosenthal Plot this graph can be used to visualize a two-site fit. The most accurate analysis of the data comes from nonlinear regression analysis using the equation for a sigmoid curve.

An F-test is used to determine whether the data fits a one-site model better than a two site model.

The F-test is used to compare fits to the one-site and the two-site model. The computer program Prism (GraphPad, Inc.) will do this automatically. The basic steps are

• Analyze the data for a one- and two-site fit using nonlinear regression analysis.
• Use the following equation to determine the F value.

where SS1 = sum of squares for one-site fit
SS2 = sum of squares for two-site fit
DF1 = degrees of freedom for one-site fit
DF2 = degrees of freedom for two-site fit

• Determine the P value from a F-table of statistics.
• The P value answers the question:

  If model 1 (one-site fit) is correct, what is the chance that you would randomly obtain data that fits model 2 (two-site fit) much better?

• If p is low, you conclude that model 2 (two-site fit) is significantly better than model 1.
• The competition curve for a saturation experiment looks like this:

The data was analyzed with both a one-site and two-site fit and gave the following results:

SS1 = 17050
SS2 = 1.923 x 10^-7
DF1 = 27
DF2 = 25

Applying this data to the F equation gives:

F = 1.109 x 10¹²
P = < 0.0001

This means the data fit a two-site model better than a one-site model.