A simple reaction scheme for the interaction of an agonist [A] with its receptor [R] can be described as:

Rate of forward reaction:

Rate of reverse reaction:

If the system is at equilibrium and [A] >> [R] (in other words, there isn’t any ligand depletion), then the rate of reaction is proportional to the product of the concentration of the reactants, i.e.

, so let’s find [AR]

If , then

or , but we can’t measure [R], so let’s simplify further

We know that or

Thus

Simplify for [AR],

which can also be written as –

or

where represents the proportion of occupied receptors

We can use this equation to understand the relationship between ligand concentration [A] and receptor occupancy –

At 50% receptor occupancy

or ,

in other words, at 50% receptor occupancy, the concentration of the ligand [A] is equal to it’s .

*Related*