Pharmacology

Antagonism Simulator

Models how a competitive, non-competitive or uncompetitive antagonist changes the response to an agonist, and the Schild dose ratio it produces.

Predicted effect

71.4% of Emax

EC₅₀ shift factor 2.00×

Competitive

The antagonist competes for the same site, so enough agonist still reaches the full effect — the curve shifts right without losing height.

Antagonism type

Parameters

Concentrations and affinities. Affinity k is the reciprocal of the dissociation constant Kd.

Agonist [A]

µM

Concentration of agonist at the receptor.

Antagonist [B]

µM

Set to 0 to see the agonist alone.

Agonist affinity kₐ

µM⁻¹

Kd(A) = 1/kₐ = 2.00 µM

Antagonist affinity k_b

µM⁻¹

Kd(B) = 1/k_b = 5.00 µM

Maximal response Emax

The system's ceiling with no antagonist present.

Try an example

Working

The occupancy calculation behind the effect.

Kd(A) = 1 / kₐ2.000µM

Kd(B) = 1 / k_b5.000µM

Fractional occupancy0.7143

Effect = occupancy × Emax71.4%

EC₅₀ shift (dose ratio)2.00×

Rightward shift

Dose-response curve

Effect against log agonist concentration, expressed relative to Kd(A). The dashed line is the same agonist with no antagonist present.

Effect is taken as fractional receptor occupancy multiplied by Emax. Affinities are entered as k, so Kd = 1/k throughout.

Competitive — the Gaddum equation. The antagonist raises the apparent Kd of the agonist but not the ceiling:

occupancy = [A] / ([A] + Kd(A) × (1 + [B]/Kd(B)))

The bracketed term is the Schild dose ratio: the factor by which the agonist concentration must rise to restore the original effect.

dose ratio = 1 + [B] / Kd(B)

Non-competitive — occupancy of the agonist site is unchanged, but a fraction of receptors is removed from the pool, lowering the attainable maximum:

occupancy = [A]/([A] + Kd(A)) × (1 − [B]/([B] + Kd(B)))

Uncompetitive — written here as [A]/([A]+Kd(A)) × Kd(B)/(Kd(B)+[B]), which is the same expression rearranged, so it returns the same value as the non-competitive case.

Common questions

It is the dose ratio: how many times more agonist is needed, in the presence of the antagonist, to produce the effect the agonist alone produced. A factor of 2 means the concentration must double. It is only defined for competitive antagonism, so the other two modes show 1.00×.

Because the block is surmountable. Agonist and antagonist compete for the same site, so raising the agonist concentration far enough restores full occupancy — the curve moves right but does not get shorter.

Enter its reciprocal. A Kd of 2 µM is an affinity of 0.5 µM⁻¹; a Kd of 5 µM is 0.2 µM⁻¹. The calculated Kd is shown under each affinity field so you can check it.

Because the two expressions used here are algebraically identical. This is a limitation of the model, flagged on screen rather than silently changed; a genuine uncompetitive antagonist would lower Emax and also shift the EC₅₀ to the left.

About receptor antagonism

An antagonist reduces the effect of an agonist, but how it does so depends on where it binds. The three classical cases differ in whether more agonist can overcome the block — and that difference is what a dose-response curve reveals.

Use it when

Learning why a competitive block shifts the curve right but keeps Emax

Interpreting a Schild plot or a dose-ratio experiment

Seeing how antagonist affinity changes the size of the shift

Keep in mind

This is a teaching model of receptor occupancy. It assumes occupancy equals effect, with no spare receptors, no signal amplification and no partial agonism.

Affinities are entered as k (1/µM), so the dissociation constant Kd used in the equations is 1/k.

The non-competitive and uncompetitive options currently produce identical numbers — see the note below the result.

Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy