Competitive binding to two receptor types

Competitive binding with two sites with the same affinity for the radioligand

Included in the list of built-in equations of Prism is "Competitive binding (two sites)". This equation fits data for the fairly common situation where:

	•	There are two distinct classes of receptors. For example, a tissue could contain a mixture of b1 and b2 adrenergic receptors.

	•	The unlabeled ligand has distinct affinities for the two sites.

	•	The labeled ligand has equal affinity for both sites. (If you are not willing to make this assumption, see Competitive binding to two receptor types .

	•	Binding has reached equilibrium.

	•	A small fraction of both labeled and unlabeled ligand bind. This means that the concentration of labeled ligand that you added is very close to the free concentration in all tubes.

When you look at the competitive binding curve, you will only see a biphasic curve in unusual cases where the affinities are extremely different. More often you will see a shallow curve with the two components blurred together. For example, the graph below shows competition for two equally abundant sites with a ten fold (one log unit) difference in EC50. If you look carefully, you can see that the curve is shallow (it takes more than two log units to go from 90% to 10% competition), but you cannot see two distinct components.

Comparing one- and two-site models

Prism can simultaneously fit your data to two equations and compare the two fits. This feature is commonly used to compare a one-site competitive binding model and a two-site competitive binding model. Since the model has an extra parameter and thus the curve has an extra inflection point, the two-site model almost always fits the data better than the one site model. And a three-site model fits even better. Before accepting the more complicated models, you need to ask whether the improvement in goodness of fit is more than you'd expect by chance. Prism answers this question with an F test. The resulting P value answers this question: If the one site model were really correct, what is the chance that randomly chosen data points would fit to a two-site model this much better (or more so) than to a one-site model. See Comparing the fits of two models

Before looking at Prism's comparison of the two equations, you should look at both fits yourself. Sometimes the two-site fit gives results that are clearly nonsense. For example, disregard a two-site fit when:

	•	The two IC50 values are almost identical.

	•	One of the IC50 values is outside the range of your data.

	•	The variable FRACTION is close to 1.0 or to 0.0. In this case, virtually all the receptors have the same affinity, and the IC50 value for the other site will not be reliable.

	•	The variable FRACTION is negative or greater than 1.0.

	•	The best-fit values for BOTTOM or TOP are far from the range of Y values observed in your experiment.

Competitive binding to two receptor types with different affinities for the radioligand

The standard equation for competitive binding to two sites assumes that the labeled ligand has equal affinity for both sites. It is easy to derive an equation for situations where the labeled ligand binds differently to the two sites.

This is the standard equation for competitive binding to one site:

Binding is the sum of specific and nonspecific binding. To create an equation for two sites, you simply need to create an equation with two specific binding components with different values for Bmax, Kd, and Ki.:

;Enter data with X=log[unlabeled] and Y=CPM
ColdnM=10^(X+9)
KI1nM = 10^(LogKI1+9)
KI2nM = 10^(LogKI2+9)
SITE1= HotnM*Bmax1/(HotnM + KD1*(1+coldnM/Ki1nM))
SITE2= HotnM*Bmax2/(HotnM + KD2*(1+coldnM/Ki2nM))
Y = SITE1 + SITE2 + NSCPM
Select this equation from the Advanced Radioligand Binding equation library.

Notes:

	•	This equation does not account for ligand depletion. It assumes that the free concentration equals the added concentration.

	•	When using this equation to fit data, you will need to assign constant values to KD1 and KD2, the KD of the hot ligand for the two sites. You will need to obtain these values from other experiments. Perhaps you can isolate tissue with only one of the receptor types and measure KD in that preparation.