Hill Equation & Cooperativity

Hill Parameters

Hill coefficient n: 2.8 K_d (half-saturation): 2.6 [L] probe (current [O₂]): 5.0

Legend

Hemoglobin (n≈2.8)

Myoglobin (n=1)

Custom (n slider)

Probe [L]

At Probe [L]

θ (custom): —

θ (Hemoglobin): —

θ (Myoglobin): —

P₅₀ (Hb): 2.6 mmHg

P₅₀ (Mb): 0.5 mmHg

Physics

Hill (1910) derived the saturation curve for cooperative binding. n=1: no cooperativity (Langmuir). n>1: positive cooperativity — binding of one ligand promotes further binding (allosteric effect). Hemoglobin (n≈2.8) vs myoglobin (n=1) demonstrates cooperative O₂ loading/unloading. The Hill plot (log(θ/(1−θ)) vs log[L]) linearizes with slope n.