A Mathematical Model for Inter-Cellular Inductive Notch Signaling

In vertebrate limb, a group of specialized epithelial cells called Apical Ectodermal Ridge (AER) form at the boundary of dorsal and ventral limb ectoderm. Recent experiments suggest that AER forms at the boundary of Fringe expressing and Fringe non-expressing cells by a specific type of receptor-ligand interaction called as inductive signaling, involving the transmembrane proteins Notch, Serrate and Delta. Experiments conducted on Drosophila wing disc have shown that Fringe inhibits the binding ability of Serrate ligand to Notch and enhances that of Delta to Notch. Although several of the signaling elements have been identified experimentally, it remains unclear how the inter-cellular interactions can give rise to such a boundary of specialized cells. Here we present an ordinary differential equation (ODE) model involving Delta→Notch and Serrate→Notch interactions between juxtaposed Fringe expressing and Fringe nonexpressing cells. When simulated in a compartmentalized set up, this model gives rise to high Notch levels at the boundary of Fringe expressing and Fringe non-expressing cells.