Chemical Master Equation — Stochastic Reaction Networks

Reaction Network: A ⇌ B (Toggle)

k₊ (A→B): 0.10 k₋ (B→A): 0.05 Production rate k_on: 0.20 Degradation rate k_deg: 0.03 System size Ω: 20

Statistics

Mean ⟨n⟩: –
Variance σ²: –
Fano factor: –
Gillespie steps/s: –

The CME gives exact P(n,t) for integer molecule counts. Unlike ODEs, it captures intrinsic noise — crucial when n is small. Gillespie's SSA samples exact CME trajectories via exponential waiting times. Fano=σ²/⟨n⟩: Poisson=1, sub-Poissonian<1, bursty>1.