Rate Constants

Concentrations

Substrate [S]
100
Enzyme [E]
10
Complex [ES]
0
Product [P]
0

Michaelis-Menten

E + S ES E + P
Km = (k-1 + kcat) / k1 = 60
Vmax = kcat * [E]total = 5

Concentrations Over Time

Substrate [S]
Enzyme [E]
Complex [ES]
Product [P]

Reaction Rate (v = d[P]/dt, saturation curve)

How It Works

The Michaelis-Menten model describes how enzymes catalyze reactions. The Petri net has 4 places and 3 transitions:

  • bind (k1): substrate + enzyme → complex
  • unbind (k-1): complex → substrate + enzyme (reverse)
  • catalyze (kcat): complex → product + enzyme

Mass-action kinetics on this net automatically produce the Michaelis-Menten equations. At steady state, the reaction rate follows:

v = Vmax * [S] / (Km + [S])

The rate saturates at Vmax because all enzyme molecules become occupied (the complex reaches its maximum). Km is the substrate concentration at half-maximum rate.