Stochastic Gene Expression — Master Equation

Bursty mRNA production: gene ON/OFF switching + Poisson transcription + degradation

k_on (activation): 0.3

k_off (repression): 1.0

Transcription k_r: 5.0

Degradation γ: 0.5

Mean mRNA: —

Variance: —

Fano factor: —

Theory ⟨n⟩: —

Theory Fano: —

Gillespie SSA simulation. Gene switches ON→OFF (k_off) and OFF→ON (k_on). mRNA produced at k_r when ON, degraded at γ·n. Beta-Poisson mixture: Fano = 1 + k_r·k_off/((k_on+k_off)·(k_on+k_off+γ)).