Intro to Pharmacology and Toxicology Topics   

Receptor Antagonists

A simple bimolecular association model involving a receptor and a ligand can be describe by:

[R] + [L] [RL]

d[RL] / dt = k1 [R] [L] - k-1 [RL]

If another ligand with affinity for the receptor is added to the system, two simultaneous equilibria must be considered:

[R] + [L] [RL]      AND     [R] + [A] [RA]

If the second ligand A has no efficacy, it is an antagonist: a ligand that blocks the effect of an agonist on a receptor. The antagonist will have affinity for the receptor but no efficacy. The equilibrium binding equation in the presence of both agonist and antagonist can be derived by recalling that vf = vr at equilibrium, therefore:

k1 [R] [L]   =   k-1 [RL]      AND     k2 [R] [A]   =   k-2 [RA]

Since conservation of mass dictates that [R]total = [R] + [RL] + [RA]:

k1 ([R]total - [RL] - [RA]) [L]   =   k-1 [RL]

The same steps can be applied to the equilibrium of [A] in order to obtain an analogous equation. By combining the equations and defining Kd = k-1/k1 and Ki = k-2/k2 we obtain an expression describing the effects of agonist binding at equilibrium in the presence of antagonist:

[RL]  =         [R]total [L]total     
              (1+[A]/Ki)Kd + [L]total    

This equation describes a simple competitive or surmountable antagonist, whose action is capable of being blocked by an excess of agonist.

The effects of a noncompetitive or unsurmountable antagonist cannot be fully reversed by excess agonist. Noncompetitive antagonists may be reversibly or irreversibly bound to the receptor. The following scheme describes a reversibly noncompetitive antagonist, assuming that any form of the receptor bound to antagonist A is inactive.

                     k1
   [R] + [L] [RL]
    +               k-1       +
   [A]                       [A]
k-2k2                 k-2k2
  [RA]                   [RLA]

The equation describing agonist binding at equilibrium in the presence of reversible noncompetitive antagnist is:

[RL]  =          [R]total [L]        
              (1+[A]/Ki) (Kd + [L])

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