Juxatcrine 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. I will discuss two mathematical models for this signalling mechanism, which use different mathematical representations of the local averaging that is implicit in a juxtacrine mechanism. Biologically, a key issue is the the ability of a juxtacrine signal to transmit over large distances, and I will show how this can be calculated via linear analysis of the models. I will also show that in appropriate parameter regimes, the juxtacrine mechanism can support spatial patterns on the scale of a few cells lengths. I will illustrate the results with numerical simulations for the particular case of the TGF-alpha -- EGF-R juxtacrine interaction.
Joint work with Markus Owen, Helen Wearing, and Simon Myers.