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In quorum sensing (QS), bacteria exchange molecular signals to work together.An analytically-tractable model is presented for characterizing QS signalpropagation within a population of bacteria and the number of responsivecooperative bacteria (i.e., cooperators) in a two-dimensional (2D) environment.Unlike prior works with a deterministic topology and a simplified molecularpropagation channel, this work considers continuous emission, diffusion,degradation, and reception among randomly-distributed bacteria. Usingstochastic geometry, the 2D channel response and the corresponding probabilityof cooperation at a bacterium are derived. Based on this probability, newexpressions are derived for the moment generating function and different ordersof moments of the number of cooperators. The analytical results agree with thesimulation results obtained by a particle-based method. In addition, thePoisson and Gaussian distributions are compared to approximate the distributionof the number of cooperators and the Poisson distribution provides the bestoverall approximation. The derived channel response can be generally applied toany molecular communication model where single or multiple transmitterscontinuously release molecules into a 2D environment. The derived statistics ofthe number of cooperators can be used to predict and control the QS process,e.g., predicting and decreasing the likelihood of biofilm formation.

Characterization of Cooperators in Quorum Sensing with 2D Molecular Signal Analysis