Stochastic Gene Expression — Bimodal Distributions

Chemical master equation simulation of bistable gene circuits — noise-induced switching between ON/OFF states

Protein count

OFF

State

Switches

—

Burst size

Basal rate k_0 0.20

Active rate k_1 8.0

Degradation δ 0.10

Feedback Hill n 2.0

Half-max K 20

Burst size b 3.0

Bistable gene circuits exhibit bimodal protein distributions via positive feedback: dP/dt = k₀ + k₁·Pⁿ/(Kⁿ+Pⁿ) - δP. Gillespe SSA simulation captures intrinsic noise — bursts of mRNA/protein production cause stochastic switching between LOW and HIGH expression states. This explains cell-to-cell variability in isogenic populations.