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 (a_i) of the substance within each cell. The cells are balls of radius (R) in (mathbb {R} ^3) , 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.