A dynamical model of ommatidial crystal formation.

ABSTRACT

The crystalline photoreceptor lattice in the Drosophila eye is a paradigm for pattern formation during development. During eye development, activation of proneural genes at a moving front adds new columns to a regular lattice of R8 photoreceptors. We present a mathematical model of the governing activator-inhibitor system, which indicates that the dynamics of positive induction play a central role in the selection of certain cells as R8s. The "switch and template" patterning mechanism we observe is mathematically very different from the well-known Turing instability. Unlike a standard lateral inhibition model, our picture implies that R8s are defined before the appearance of the complete group of proneural cells. The model reproduces the full time course of proneural gene expression and accounts for specific features of the refinement of proneural groups that had resisted explanation. It moreover predicts that perturbing the normal template can lead to eyes containing stripes of R8 cells. We observed these stripes experimentally after manipulation of the Notch and scabrous genes. Our results suggest an alternative to the generally assumed mode of operation for lateral inhibition during development; more generally, they hint at a broader role for bistable switches in the initial establishment of patterns as well as in their maintenance.