Two-state promoter model: transcriptional bursting from chromatin dynamics
Two-state promoter model (Raj & van Oudenaarden 2008):
Each gene promoter randomly switches between active (ON, green) and inactive
(OFF, dark) states at rates k_on and k_off. When ON, mRNA molecules are produced in geometric
bursts of mean size b = k_transcription / k_off. Each mRNA degrades at rate μ.
This produces non-Poissonian noise: the mRNA distribution is negative binomial
(not Poisson), with noise CV² = 1/⟨n⟩ + 1/b. Large burst size → broad, heavy-tailed distribution
(heterogeneity). This is measured experimentally via single-molecule FISH. The histogram (right)
updates in real-time showing the steady-state distribution across N cells.