  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 signaling 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 cooperative bacteria in a variety of QS-coordinated
activities, e.g., biofilm formation and antibiotic resistance.
