Hill Equation (Dose-Response)

E = E_{\max} \frac{[L]^n}{K_d^n + [L]^n}

Drug effect saturates sigmoidally with ligand concentration—cooperativity via Hill coefficient n.

By Archibald Hill

Medical Sciences

1910 · Archibald Hill

Why it matters: Standard model for drug dosing, receptor binding, and EC50 determination.

Discoverers: Archibald Hill (1910)

What does it mean?

Drug effect saturates sigmoidally with ligand concentration—cooperativity via Hill coefficient n.

Standard model for drug dosing, receptor binding, and EC50 determination.

Symbol	Name	Unit	Meaning
$E$	Effect	—	Biological response
$E_max$	Max effect	—	Maximum response
$K_d$	Dissociation constant	—	Half-max concentration
$n$	Hill coefficient	—	Cooperativity

n>1: steep dose-response (cooperative); n=1: Michaelis-Menten-like.

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E = E_{\max} \frac{[L]^n}{K_d^n + [L]^n}

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Drug effect saturates sigmoidally with ligand concentration—cooperativity via Hill coefficient n.

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