Optimality and robustness in quorum sensing (QS)-mediated regulation of a costly public good enzyme.

Bacteria secrete a variety of public good exoproducts into their environment. These exoproducts are typically produced under the control of quorum sensing (QS), a signaling mechanism by which bacteria sense and respond to changes in their density. QS seems to provide an advantageous strategy to regulate these costly but beneficial exoproducts: it delays production until sufficiently high cell density, when the overall benefit of exoproducts outweighs cost of their production. This notion raises several fundamental questions about QS as a general control strategy adopted by bacteria. How much delay is advantageous? Under what conditions does QS-mediated regulation become advantageous? How does this advantage depend on the kinetic properties of QS? How robust is a given QS system to the stochastic events that occur over bacterial lifecycles? To quantitatively address these questions, we engineered a gene circuit in Escherichia coli to control the synthesis and secretion of a costly but beneficial exoenzyme. We show that exoenzyme production is overall advantageous only if initiated at a sufficiently high density. This property sets the potential advantage for QS-mediated regulation when the initial density is low and the growth cycle is sufficiently long compared with the exoenzyme response time. This advantage of QS-mediated regulation is robust to varying initial cell densities and growth durations, and it is particularly striking when bacteria face uncertainty, such as from stochastic dispersal during their lifecycle. We show, however, that, for QS to be optimal, its kinetic properties must be appropriately tuned; this property has implications for antibacterial treatments that target QS.