Feedback-induced counterintuitive correlations of gene expression noise with bursting kinetics

Previous studies showed that a higher frequency of bursting results in lower expression noise whereas a larger size of bursting leads to higher expression noise. Here, we show counterintuitive correlations of expression noise with bursting kinetics due to the effect of feedback. Specifically, in the case of increasing the negative feedback strength but keeping the mean expression fixed, both the mean burst frequency and the mean burst size are invariant if the off-switching rate decreases, but expression noise is reduced; or the mean burst frequency is invariant and the burst size decreases if the transcription rate increases, but expression noise is amplified. Similarly, in the case of increasing the positive feedback strength but keeping the mean expression fixed, both the mean burst frequency and the mean burst size are invariant if the on-switching rate decreases; or the mean burst frequency increases and the mean burst size is invariant if the leakage rate decreases, but expression noise is amplified. In addition, we find that the previous conclusion that a larger burst size results in the lower noise in burst size needs to be modified in the case of feedback. Our results not only clarify the confusing relationship between feedback and expression noise but also imply that the mRNA or protein noise is no longer a simple sum of the internal noise and the promoter noise as shown in the case of no feedback.