Bulletin of Mathematical Biology

, Volume 81, Issue 5, pp 1479–1505 | Cite as

Modeling the Role of Feedback in the Adaptive Response of Bacterial Quorum Sensing

  • Gaoyang Fan
  • Paul C. BressloffEmail author


Bacterial quorum sensing (QS) is a form of intercellular communication that relies on the production and detection of diffusive signaling molecules called autoinducers. Such a mechanism allows the bacteria to track their cell density in order to regulate group behavior, such as biofilm formation and bioluminescence. In a number of bacterial QS systems, including V. harveyi, multiple signaling pathways are integrated into a single phosphorylation–dephosphorylation cycle. In this paper, we propose a weight control mechanism, in which QS uses feedback loops to ‘decode’ the integrated signals by actively changing the sensitivity in different pathways. We first use a slow/fast analysis to reduce a single-cell model to a planar dynamical system involving the concentrations of phosphorylated signaling protein LuxU and a small non-coding RNA. In addition to identifying the weight control mechanism, we show that adding a feedback loop can lead to a bistable QS response in certain parameter regimes. We then combine the slow/fast analysis with a contraction mapping theorem in order to reduce a population model to an effective single-cell model, and show how the weight control mechanism allows bacteria to have a finer discrimination of their social and physical environment.


Quorum sensing Cell signaling Phosphorylation–dephosphorylation cycles Feedback pathways Intercellular communication 



PCB was supported by the National Science Foundation (DMS-1613048). GF was supported by the National Science Foundation (DMS-RTG 1148230).


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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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