Mathematical Model of Quorum Sensing and Biofilm

Bacteria are unicellular microorganism, which are found in nature quite often. They talk to each other using chemical signaling process (quorum sensing) and ion-channel mediated electrical signaling mechanism. Quorum sensing is a density dependent bacterial collective behaviour and/or cell-to -cell communication mechanism. This widespread bacterial behaviour is related with biofilm formation, gene expression, swarming, virulence and bioluminescence. In a recent realization (experimental and theoretical study), it was observed that bacteria can also talk to each other through the wave of potassium and an oscillatory dynamics was noticed in bacterial biofilms. In this present chapter, we present two different mathematical frameworks of bacterial communication system. The first model is based on the bacterial density dependent behaviour with up-regulation and down-regulation of the production of quorum sensing molecules. Second model, we introduce two different types of the bacterial communication process within a mathematical framework, which is also related to the biofilm formation. This mathematical framework combine quorum sensing mechanism as well as electrical signaling process. We discuss different spatiotemporal patterns and chaotic behaviour in this communication system. Moreover, it gives a significant and the fundamental role of noise in the complex biological conversation system. Finally we propose some open problem in the last section of this chapter, which are helpful for the future research of the bacterial communication system.