Gillespie Algorithm

Exact Stochastic Simulation of Chemical Kinetics

Reaction System

∅ →k₁ A
A →k₂
2A →k₃ A + B
B →k₄

State

A molecules
B molecules
Sim time t
Events / step
Mean A (theory)
Gillespie (1977): The exact stochastic simulation of master equations. Draw time τ from exponential distribution with rate Σaᵢ, choose reaction μ with prob aμ/Σaᵢ. No approximations — captures intrinsic molecular noise that ODEs miss. Crucial for gene expression, cell signaling with low copy numbers.