The bacteria Pseudomonas aeruginosa use the size and density of their colonies to regulate the production of a large variety of substances, including toxins. This phenomenon, called quorum sensing, apparently enables colonies to grow to sufficient size undetected by the immune system of the host organism.
In this paper, we present a mathematical model of quorum sensing in P. aeruginosa that is based on the known biochemistry of regulation of the autoinducer that is crucial to this signalling mechanism. Using this model we show that quorum sensing works because of a biochemical switch between two stable steady solutions, one with low levels of autoinducer and one with high levels of autoinducer.
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Dockery, J.D., Keener, J.P. A mathematical model for quorum sensing in Pseudomonas aeruginosa . Bull. Math. Biol. 63, 95–116 (2001). https://doi.org/10.1006/bulm.2000.0205