The Hill equation models sigmoidal binding curves in allosteric proteins. The Hill coefficient n quantifies cooperativity: n=1 is Michaelis-Menten, n>1 is positive cooperativity.
Binding Curve θ([L])
Current Hill curve θ = [L]ⁿ / (Kⁿ + [L]ⁿ)
n=1 (Michaelis-Menten)
Operating point ([L], θ)
Parameters
θ = [L]ⁿ / (Kⁿ + [L]ⁿ)
Derived Quantities
Occupancy θ0.500
Sensitivity d θ/d[L]---
EC₁₀ (10% sat.)---
EC₉₀ (90% sat.)---
EC₉₀/EC₁₀ ratio---
Cooperativity type---
Allosteric context:
Hemoglobin: n ≈ 2.8 (O₂)
CaM kinase II: n ≈ 8 (Ca²⁺)
n=1: Michaelis-Menten
n→∞: switch-like (step fn)