(a) Minimal model of EGFR signalling. The dynamics of the EGFR/Rhomboid/Spitz feedback loop is condensed in a single component ‘E’ (green), which is diffusible between cells and able to self-activate (for details, see Appendix 1). This single component represents a proxy for the activity of the feedback loop shown in Figure 1c, for example the local concentration of the active form of Spitz. The corresponding reaction-diffusion system, Equation 1, can give rise to a propagating front that leaves behind an elevated signalling state. Plots show the numerical solution of Equation 1 in a one-dimensional representation of tissue (for simplicity) at two time points with initially elevated levels of E at the left-hand side of the domain. Specifying position in units of the diffusion length and time in units of the decay time , the remaining chosen parameters are and . (b) Model of EGFR signalling interacting with the proneural gene l’sc. EGFR signalling activates L’sc expression (component ‘L’, blue), which effectively inhibits EGFR signalling by driving the NE to NB transition (for details, see Appendix 2). The corresponding reaction-diffusion system, Equation 2, can give rise to a propagating localised pulse of signalling activity and proneural gene expression corresponding to the transition zone. Parameters for E are the same as in panel a; parameters for L are , . (c) Schematic depiction of the mechanism giving rise to a localised transition zone, shown in panel b. Diffusion of signalling components (E, green) into the neuroepithelium leads to activation of the positive feedback loop, which locally excites signalling and proneural gene expression (L, blue) (Materials and methods). The excitation ceases as downregulation of signalling occurs, a consequence of the transition triggered by L’sc expression. (d) Regulatory network of the refined model including Delta-Notch signalling (D and N) and a local variable indicating the cell state ( indicates neuroepithelial cells and indicates neuroblasts; for details, see Appendix 3). Each shaded cell indicates one lattice site corresponding to one cell of the tissue. (e) Simulation of the integrated model of EGFR signalling, L’sc expression, Delta-Notch signalling and the NE to NB transition in a one-dimensional array of cells. The emerging spatial signalling and gene expression profile is characterised by a pulse of EGFR signalling, L’sc and Delta, and a drop in Notch signalling activity within the transition zone. The drop in Notch is preceded by a pulse of Notch signalling activity (pink arrowheads), which is due to a local lateral inhibition effect mediated by Delta-Notch signalling. Parameters are given in Appendix 3—table 1 except for .