Modeling the E. coli σ^E network reveals context-dependent feedback sign and kinetic constraints in the envelope stress response

The bacterial cell envelope is a structure that provides mechanical stability, serves as a barrier, determines cell size and shape, and accommodates essential cellular processes. Consequently, maintaining envelope homeostasis under stress conditions is vital for cell survival. For example, when under stress, E. coli activates the alternative σ^E factor, which induces the transcription of a regulon to restore envelope homeostasis. The molecular details of σ^E activation are well characterized. Conversely, the combined effects of transcriptional and post-translational regulation of σ^E are less understood and no comprehensive model of the system has been established. Here, we combine modeling with synthetic biology to determine the regulatory mechanisms of the σ^E network. The results suggest that the presence of autoregulation leads to a feedback gain switch from negative to positive when cells are exposed to stress. In addition, our results suggest that the RseA degradation rate changes gradually rather than instantaneously upon stress. Finally, maintaining σ^E activity under excess RseA and high binding affinity requires a low complex formation rate. In summary, our findings elucidate the regulatory mechanisms controlling the σ^E stress response, thereby advancing the understanding of σ-factor bacterial networks.