Enzyme Kinetics: Michaelis-Menten & Cooperativity
Hill Equation · Sigmoidal Response · Allostery · Lineweaver-Burk
Hill n=1 (MM)
Hill n=2
Hill n (custom)
½Vmax line
Parameters
Vmax (μM/s)
10
Km (Michaelis constant, μM)
5
Hill coefficient n
2.5
[S] range max (μM)
40
½Vmax at [S]
—
EC50 (Hill)
—
Cooperativity
—
Michaelis-Menten (n=1):
v = Vmax·[S] / (Km + [S])
Hill Equation (cooperative):
v = Vmax·[S]ⁿ / (Kmⁿ + [S]ⁿ)
Cooperativity index:
n > 1
: positive cooperativity
n = 1
: Michaelis-Menten
n < 1
: negative cooperativity
Hill plot (linear):
log(θ/(1-θ)) = n·log[S] − n·log K½