Modeling stochastic gene expression under repression.

Intrinsic transcriptional noise induced by operator fluctuations is investigated with a simple spin-like stochastic model. The effects of transcriptional fluctuations in protein synthesis are probed by coupling transcription and translation by an amplificative interaction. In the presence of repression a new term contributes to the noise, which depends on the rate of mRNA production. If the switch decay time is small compared with the mRNA life time, the noise is also small. In general the damping of protein production by a repressive agent occurs linearly but fluctuations can show a maximum at intermediate repression. The discrepancy among the switch decay time, the mRNA degradation, and protein degradation is crucial for the repressive control in translation without large fluctuations. The noise profiles obtained here are in quantitative agreement with recent experiments.