Question

Estimate the binding affinity of a ligand for its receptor from the following data:

[Ligand] (𝛍M)	Fractional saturation, Y
1	0.20
2	0.36
4	0.54
6	0.62
8	0.70

Short answer

Plotting the Ligand and Fraction Saturation values on a graph with the X- and Y-axes, respectively, results in a hyperbola.

Step-by-step solution

Formula for binding affinity

$$\begin{gathered} \text{Y}=\frac{\left[\text{L}\right]}{\text{KA + [L]}} \\ \Rightarrow \text{KA =}\frac{\text{[L]}}{\text{Y}}-[\text{L]} \end{gathered}$$

Where, Y stands for fractional saturation

L stands for Ligand concentration

And, K_A stands for the binding affinity

Calculation of binding affinity

Binding Affinity can be calculated as follows:

$\text{KA =}\frac{\text{[L]}}{\text{Y}}-[\text{L]}$

1. Binding affinity of a ligand with concentration 1𝛍M and Fractional saturation 0.20 is$\frac{1}{0.20}-1=4$
2. Binding affinity of a ligand with concentration 2𝛍M and Fractional saturation 0.36 is$\frac{2}{0.36}-2=3.56$
3. Binding affinity of a ligand with concentration 4𝛍M and Fractional saturation 0.0.54 is $\frac{4}{0.54}-4=3.40$
4. Binding affinity of a ligand with concentration 6𝛍M and Fractional saturation 0.62 is$\frac{6}{0.62}-0.62=3.67$
5. Binding affinity of a ligand with concentration 8𝛍M and Fractional saturation 0.70 is$\frac{8}{0.70}-8=3.42$

Graphical representation

A graph is plotted with the ligand concentration representing the X-axis and the Fractional saturation as the Y-axis.

Hence, the predicted value of 0.5Y is equivalent to a K_L (ligand concentration), of roughly 0.5µM.