An approximative approach for single cell spatial modeling of quorum sensing

Quorum sensing, a special kind of cell-cell communication, has originally been described for well-mixed homogeneous bacterial cultures. However, recent perception supports its ecological relevance for spatially heterogeneous distributed cells, like colonies and biofilms. New experimental techniques allow for single cell analysis under these conditions, which is crucial to understanding the effect of chemical gradients and intercell variations. Based on a reaction-diffusion system, we develop a method that drastically reduces the computational complexity of the model. In comparison to similar former approaches, handling and scaling is much easier. Via a suitable scaling, this approach leads to approximative algebraic equations for the stationary case. This approach can be easily used for numerical situations.