Gene Expression — Two-State Promoter Noise

The two-state promoter model (telegraph process) captures transcriptional bursting: the gene randomly switches ON/OFF, producing bursty mRNA and protein distributions far from Poisson.

ON rate (k_on)0.30
OFF rate (k_off)0.50
Transcription rate (k_tx)3.0
Degradation rate (δ)0.50
Gene: OFF ⇌(k_on/k_off) ON
ON → mRNA (rate k_tx)
mRNA → ∅ (rate δ)

Mean ⟨m⟩ = k_tx·k_on/(δ(k_on+k_off))
Fano = 1 + k_tx·k_off/(δ(k_on+k_off+δ))
(Fano > 1 = super-Poisson bursting)
Mean: —
Fano: —
State: —