Respuesta :
Answer : The value of [tex]K_d[/tex] for the receptor-ligand interaction is [tex]27.9\mu M[/tex]
Explanation :
The equilibrium reaction between receptor and ligand will be:
[tex]R+L\overset{K_f}\rightarrow [RL][/tex] (forward reaction)
[tex][RL]\overset{K_d}\rightarrow R+L[/tex] (backward reaction)
where,
R = receptor
L = ligand
[RL] = receptor-ligand complex
As we know that,
[tex]K_f=\frac{1}{K_d}[/tex]
The expression of [tex]K_f[/tex] is:
[tex]K_f=\frac{[RL]}{[R][L]}[/tex]
As we are given that:
Total [R] = [tex]50\mu M[/tex]
Total [L] = [tex]100\mu M[/tex]
Free [R] = [tex]15\mu M[/tex]
Bound [R] = [tex]50-15=35\mu M[/tex]
Bound [L] = Bound [R] = [tex]35\mu M[/tex]
Free [L] = [tex]100-35=65\mu M[/tex]
Now put all the given values in above expression, we get:
[tex]K_f=\frac{[RL]}{[R][L]}[/tex]
[tex]K_f=\frac{(35)}{(15)(65)}[/tex]
[tex]K_f=0.0358\mu M^{-1}[/tex]
Now we have to calculate the value of [tex]K_d[/tex] for the receptor-ligand interaction.
[tex]K_f=\frac{1}{K_d}[/tex]
[tex]0.0358\mu M^{-1}=\frac{1}{K_d}[/tex]
[tex]K_d=27.9\mu M[/tex]
Therefore, the value of [tex]K_d[/tex] for the receptor-ligand interaction is [tex]27.9\mu M[/tex]
