Overlaid positive and negative feedback loops shape dynamical properties of PhoPQ two-component system

Bacteria use two-component systems (TCSs) to sense environmental conditions and change gene expression to adapt to those conditions. To amplify cellular responses, many bacterial TCSs are under positive feedback control, i.e. increase their own expression when activated. In E. coli, Mg2+-sensing TCS, PhoPQ, in addition to the positive feedback includes a negative feedback via upregulation of MgrB protein that inhibits PhoQ. How interplay of these feedback loops shapes steady state and dynamical responses of PhoPQ TCS to change in Mg2+remains poorly understood. In particular, how the presence of MgrB feedback affects the robustness of PhoPQ response to overexpression of TCS is unclear. It is also unclear why the steady state response to decreasing Mg2+is biphasic, i.e. plateaus over a range of Mg2+concentrations and then increases again at growth-limiting Mg2+. In this study, we use mathematical modeling to identify potential mechanisms behind these experimentally observed dynamical properties. The results make experimentally testable predictions for the regime with response robustness and propose novel explanation of biphasic response constraining the mechanisms for modulation of PhoQ activity by Mg2+and MgrB. Finally, we show how interplay of positive and negative feedback loops affect networks steady-state sensitivity and response dynamics. In the absence of MgrB feedback, the model predicts oscillations thereby suggesting a general mechanism of oscillatory or pulsatile dynamics in autoregulated TCSs. These results help better understanding of TCS signaling and other networks with overlaid positive and negative feedback. Author summaryFeedback loops are commonly observed in bacterial gene-regulatory networks to enable proper dynamical responses to stimuli. Positive feedback loops often amplify the response to stimulus, whereas negative feedback loops are known to speed-up the response and increase robustness. Here we demonstrate how combination of positive and negative feedback in network sensing extracellular ion concentrations affects its steady state and dynamic responses. We utilize published experimental data to calibrate mathematical models of the gene regulatory network. The resulting model quantitatively matches experimentally observed behavior and can make predictions on the mechanism of negative feedback control. Our results show the advantages of such a combination feedback loops and predict the effect of their perturbation on the steady state and dynamic responses. This study improves our understanding of how feedback loops shape dynamical properties of signaling networks.