The interplay of multiple feedback loops with post-translational kinetics results in bistability of mycobacterial stress response

Bacterial persistence is the phenomenon in which a genetically identical fraction of a bacterial population can survive exposure to stress by reduction or cessation of growth. Persistence in mycobacteria has been recently linked to a stress-response network, consisting of the MprA/MprB two-component system and alternative sigma factor sigma(E). This network contains multiple positive transcriptional feedback loops which may give rise to bistability, making it a good candidate for controlling the mycobacterial persistence switch. To analyze the possibility of bistability, we develop a method that involves decoupling of the network into transcriptional and post-translational interaction modules. As a result we reduce the dimensionality of the dynamical system and independently analyze input-output relations in the two modules to formulate a necessary condition for bistability in terms of their logarithmic gains. We show that neither the positive autoregulation in the MprA/MprB network nor the sigma(E)-mediated transcriptional feedback is sufficient to induce bistability in a biochemically realistic parameter range. Nonetheless, inclusion of the post-translational regulation of sigma(E) by RseA increases the effective cooperativity of the system, resulting in bistability that is robust to parameter variation. We predict that overexpression or deletion of RseA, the key element controlling the ultrasensitive response, can eliminate bistability.