A receptor is mixed with its ligand and the concentration of

A receptor is mixed with its ligand and the concentration of ligand-receptor complex is measured after the system reaches equilibrium. The total concentration of receptor is 88 nM, the total concentration of ligand is 121 nM, and the measured concentration of receptor-ligand complex at equilibrium is 75 nM. Using these values, calculate the dissociation constant, K_d.

Solution

Dissociation constant (Kd) = [R] [L] / [RL]

[R] = Concentration of free receptor at equilibrium = Total receptor R - conc. of RL complex = 88 - 75 = 5 nM

[L] = Concentration of free ligand at equilibrium = Total ligand L - conc. of RL complex = 121 - 75 = 46 nM

[RL] = Concentration of receptor - ligand complex = 75 nM

Kd = 5 x 46 / 75 = 3.06