Stochastic Petri Net — Biochemical Gillespie

Gene expression network: DNA → mRNA → Protein, with degradation. Each reaction is stochastic; the Gillespie SSA samples exact trajectories from the Chemical Master Equation. Circles=species, boxes=reactions.

Rates

k₁ transcription: 0.5 k₂ translation: 1.0 k₃ mRNA deg: 0.3 k₄ protein deg: 0.1

System State

Time: 0.0

mRNA count: 0

Protein count: 0

⟨mRNA⟩ (det): —

⟨Protein⟩ (det): —

Gillespie SSA:
a_μ = propensity of rxn μ
τ = -ln(U₁)/Σa_μ
select rxn by U₂·Σa_μ

Stochastic Petri Net — Biochemical Gillespie Algorithm

Rates

System State