Title: On the Analysis of Bacterial Cooperation with a Characterization of 2D Signal Propagation,
Abstract: 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 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. 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 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.