Modelling Quorum Sensing Mechanisms in Bacterial Populations

Quorum sensing is a cell-to-cell communication mechanism that allows bacteria to trigger collective behaviours at the population scale. In this work, we present and analyse a model for one of the quorum sensing pathways in the bacterium Pseudomonas aeruginosa. This particular pathway controls the production of elastase, which is a «public good». Public goods are metabolic costly exoproducts for the individual, but, at high enough densities, they provide an overall benefit for the whole population. The model we present is an individual-based stochastic model, that also accounts for the spatial dimensions of the system. The objective of the model is to describe the growth of wild type and mutant strains, in single and mixed populations, using an implicit representation of the bacterial exoproducts used for the interactions. The individual based model allows us to characterize and understand the growth of a wild type strain that regulates the production of public goods via a quorum sensing mechanism, as well as to address classical questions about cooperation and defection in mixed cultures: can a non-producing mutant bacteria exploit the public good benefits? Moreover, is it possible to take advantage of the communication channel to outcompete the wild type strain? Which is the role of the spatial structure in this problem, and what is the relation with the diffusion of the exoproducts? Our model is able to give qualitative answers to these questions. We will compare these answers to some of the experiments and theoretical advances in the literature.