Mathematical modelling of juxtacrine cell signalling

Juxtacrine signalling is emerging as an important means of cellular communication, in which signalling molecules anchored in the cell membrane bind to and activate receptors on the surface of immediately neighbouring cells. We develop a mathematical model to describe this process, consisting of a coupled system of ordinary differential equations, with one identical set of equations for each cell. We use a genetic representation of ligand-receptor binding, and assume that binding exerts a positive feedback on the secretion of new receptors and ligand. By linearising the model equations about a homogeneous equilibrium, we categorise the range and extent of signal patterns as a function of parameters. We show in particular that the signal decay rate depends crucially of the form of the feedback functions, and can be made arbitrarily small by appropriate choice of feedback, for any set of kinetic parameters. As a specific example, we consider the application of our model to juxtacrine signalling by TGFα in response to epidermal wounding. We demonstrate that all the predictions of our linear analysis are confirmed in numerical simulations of the non-linear system, and discuss the implications for the healing response.