A simple reaction scheme for the interaction of an agonist [A] with its receptor [R] can be described as:
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
Simplify for [AR],
which can also be written as –
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
in other words, at 50% receptor occupancy, the concentration of the ligand [A] is equal to it’s .