Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Mathematical modelling and numerical simulations of bacterial pattern formation in terms of a complex reaction-diffusion-system
Thomas Horger, Christina Kuttler, Barbara Wohlmuth

Last modified: 2014-06-09


The Staphylococcus aureus is the most common bacteria of the Staphylococcus species. It can be found almost everywhere in nature, e.g. on the skin or in the respiratory system of every human and it can cause several infections. In experiments, Staphylococcus aureus bacteria are brought onto agar plates which contain nutrients. There they grow in communities which produce biofilm and thereby form patterns. If the genes of a specific bacterium are modified, different patterns and behaviours are obtained.

In this talk, we derive a new mathematical model which is able to reproduce the different patterns formed by the bacterium Staphylococcus aureus and its mutants on an agar plate. For the modelling, we use a reaction-diffusion-system. It contains several factors which are responsible for the different patterns. Among the factors which we consider are the concentrations of active and inactive bacteria, the nutrient consumption by the bacteria as well as the production of signalling molecules and the production of biofilm. Including all these terms, the resulting reaction-diffusion-system is larger than usual reaction-diffusion- systems used for pattern formation and thus the results are more detailed and more specific patterns can be obtained. Our model can even simulate very subtle patterns in the form of a ring that can be observed on top of the main outer pattern.

Furthermore a short description of the numerical finite element method, which is used for the simulations, is given. Finally the numerical simulations of our model are compared to experimental data.