Travelling waves and other dynamical processes in a bacterial quorum sensing system

Many bacterial species and other organisms like yeast cells as well use so-called “quorum sensing” to adapt their behaviour to their local cell density and other environmental conditions via a gene regulation system. This can be mathematically described by differential equation systems including different types of feedbacks. As quorum sensing also includes extracellular diffusion of signal molecules, spatial effects may play an essential role. For that a reaction-diffusion equation is set up, where the reaction terms cover the bacterial dynamics and quorum sensing. In the thesis, a traveling wave approach is used to examine how and under which conditions the upregulation of Quorum sensing may go through a bacterial layer, in the form of a wave with constant velocity. We included different dynamical effects and considered a realistic variant of a model known from literature.