Figure 4.

Protein noise with or without transcriptional bursting. Noise in protein expression σ_p²/p̄² (variance divided by mean squared) as a function of the ratio of the sRNA and mRNA transcription rates, α_s/α_m, for different levels of transcriptional bursting. We have assumed that both the sRNAs and mRNAs are produced in bursts. The noise peaks in the crossover regimen, α_s≈α_m. A slower unbinding rate k₋ for the repressor proteins controlling sRNA and mRNA expression results in larger transcriptional bursts. Parameters are (in min⁻¹): α_m=3, α_m^on=10, α_s^on=30, τ_m=10, τ_s=30, μ=0.02, α_p=4, τ_p=30, and k₊ is adjusted to set the mean protein levels (for a discussion of parameter dependence, see Supplementary information).