Gene Expression Bursting — Stochastic Hybrid

Gene expression is a stochastic hybrid process: a gene switches discretely between ON (active) and OFF (inactive) states (telegraph model), while mRNA/protein levels evolve continuously. The result is bursty protein production — a key source of cell-to-cell variability.

k_on (gene activation): 0.30 k_off (inactivation): 0.80 k_prod (production): 4.00 k_deg (degradation): 0.50 Cells N: 80

Telegraph model: Gene OFF→ON (k_on), ON→OFF (k_off). Burst size B = k_prod/k_off. Noise CV² = 1/⟨n⟩ + 1/(1+k_on/k_off). Watch bursty single-cell traces and steady-state distribution.