Expected density of cooperative bacteria in a 2D quorum sensing based molecular communication system

The exchange of small molecular signals within microbial populations is generally referred to as quorum sensing (QS). QS is ubiquitous in nature and enables microorganisms to respond to fluctuations in living environments by working together. In this study, a QS- based molecular communication system within a microbial population in a two-dimensional (2D) environment is analytically modeled. Microorganisms are randomly distributed on a 2D circle where each one releases molecules at random times. The number of molecules observed at each randomly-distributed bacterium is first derived by characterizing the diffusion and degradation of molecules within the population. Using the derived result and some approximation, the expected density of cooperative bacteria is derived. Our model captures the basic features of QS. The analytical results for noisy signal propagation agree with simulation results where the Brownian motion of molecules is simulated by a particle- based method. Therefore, we anticipate that our model can be used to predict the density of cooperators in a variety of QS-coordinated activities, e.g., biofilm formation and antibiotic resistance.