Individual-based model for quorum sensing with background flow.

Quorum sensing is a wide-spread mode of cell-cell communication among bacteria in which cells release a signalling substance at a low rate. The concentration of this substance allows the bacteria to gain information about population size or spatial confinement. We consider a model for N cells which communicate with each other via a signalling substance in a diffusive medium with a background flow. The model consists of an initial boundary value problem for a parabolic PDE describing the exterior concentration u of the signalling substance, coupled with N ODEs for the masses ai of the substance within each cell. The cells are balls of radius R in R3, and under some scaling assumptions we formally derive an effective system of N ODEs describing the behaviour of the cells. The reduced system is then used to study the effect of flow on communication in general, and in particular for a number of geometric configurations.