Stochastic Gene Expression
Bimodal distributions from stochastic switching between gene states
Stochastic Gene Expression: Gene promoters switch stochastically between ON (active) and OFF (inactive) states. This creates cell-to-cell variability (noise) that can produce bimodal protein distributions — identical cells expressing very different protein levels.
d[mRNA]/dt = β·1_{ON} − δ·[mRNA] (plus Poisson noise)
The Fano factor (variance/mean) exceeds 1 (super-Poissonian) due to bursty production. The bimodality index depends on the ratio of switching rates to production/degradation. This is the molecular basis of phenotypic heterogeneity and bet-hedging in microbial populations.