Homework Answers
Binding of ligand to receptor protein can be represented by the chemical equilibrium
P + L <=KfKr==> PL where P = protein , L = Ligand
Kf = forward rate , Kr = reverse rate
The apparant dissociation constant
Kd = Kr / Kf = [P] [L] / [PL] -------(1)
=> [PL] = [P] [L] / Kd
the fraction of protein receptors occupied by ligand = (occupied protein / total protein) = [PL] / ([P] + [PL])
= ([P] [L] / Kd) / ([P] + ( [P] [L] / Kd))
= [P] [L] / (Kd[P] + [P] [L])
= [L] / (Kd + [L]) ----------(2)
Now when 90% of receptors have bound to ligands then θ = 0.9 & given [L] = 125μM = 0.125 mM
=> 0.9 = 0.125 / (Kd + 0.125)
=> 0.9 Kd + 0.1125 = 0.125
=> Kd = (0.0125 / 0.9)
=> Kd = 0.0139
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