The exchange of small molecular signals within microbial populations is generally referred to as quorum sensing (QS). QS is ubiquitous in nature and enables URLanisms to respond to fluctuations of living environments by working together. In this work , a QS-based  communication system within a microbial population in a two-dimensional (2D) environment is analytically modeled. Notably, the diffusion and degradation of signaling molecules within the population is characterized. URLanisms 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 analyzed. Using this analysis and some approximation, the expected density of cooperating bacteria is derived.  The analytical results are validated via a particle-based simulation method. The model can be used to predict and control behavioral dynamics of microscopic populations that have imperfect signal propagation .
The exchange of small molecular signals within microbial populations is generally referred to as quorum sensing (QS). QS is ubiquitous in nature and enables URLanisms 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. URLanisms 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 .
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Our model captures the basic features of QS.
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for noisy signal propagation agree with simulation results where the Brownian motion of molecules is simulated by
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and control behavioral dynamics of microscopic populations that have imperfect signal propagation
the density of cooperative bacteria in a variety of QS-coordinated activities, e.g., biofilm formation and antibiotic resistance