Question

You have a sample containing 1 picomole of receptor. You also have a ligand for the receptor, which has a dissociation constant (K_D) of 300 nM. If you add ligand at a concentration 300 nM, and allow the ligand and receptor to reach equilibrium, how many of the receptors are occupied? (Topic: pharmacology)

Answer 1

Let the receptor be denoted by R and ligand b denoted by L and the receptor ligand complex be denoted by RL.

Given that

The dissociation constant, k for the receptor ligand interaction given in equation above is

It can be seen that

Then,

replacing k in the dissociation constant equation by [L] gives

The fraction of receptor that are forming complex with the ligand are

Since [R] = [RL], we arrive at the conclusion that half of the receptor are occupied by ligand i.e. 0.5 picomol of receptors are occupied by ligand.