Reaction–Diffusion Equations and Their Application on Bacterial Communication

Bacteria are not just primitive stupid organisms, being only interested in divide themselves as fast as possible. Many bacterial species have developed a special kind of communication called quorum sensing which helps them to coordinate their behavior. This phenomenon is run and controlled by a special gene regulation system. It is based on production of some signal substance. From a mathematical point of view, it can be modeled, e.g., deterministically by ordinary differential equation systems. But as the signal substance can and must also leave the bacterial cells for communicating, the spread in space due to diffusion is also relevant. The diffusion equation to describe such a behavior is well known. The combination of these reaction and diffusion processes leads us to reaction–diffusion equations, which can combine these effects. Apart from some introduction in the necessary mathematical and biological background, some typical modeling questions and approaches are considered. The results may help to understand better the underlying principles and how to control them.