Counter-intuitive stochastic behavior of simple gene circuits with negative feedback.

It has often been taken for granted that negative feedback loops in gene regulation work as homeostatic control mechanisms. If one increases the regulation strength a less noisy signal is to be expected. However, recent theoretical studies have reported the exact contrary, counter-intuitive observation, which has left a question mark over the relationship between negative feedback loops and noise. We explore and systematically analyze several minimal models of gene regulation, where a transcriptional repressor negatively regulates its own expression. For models including a quasi-steady-state assumption, we identify processes that buffer noise change (RNA polymerase binding) or accentuate it (repressor dimerization) alongside increasing feedback strength. Moreover, we show that lumping together transcription and translation in simplified models clearly underestimates the impact of negative feedback strength on the system's noise. In contrast, in systems without a quasi-steady-state assumption, noise always increases with negative feedback strength. Hence, subtle mathematical properties and model assumptions yield different types of noise profiles and, by consequence, previous studies have simultaneously reported decrease, increase or persistence of noise levels with increasing feedback. We discuss our findings in terms of separation of timescales and time correlations between molecular species distributions, extending current theoretical findings on the topic and allowing us to propose what we believe new ways to better characterize noise.