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.