Professor David K. Lubensky
Department of Physics
University of Michigan

Patterning Neurogenesis: A dynamical model of ommatidial crystal formation

Abstract:

Regular patterns of cell fate appear widely in biology. I will present a quantitative analysis of one of the classic examples of such pattern formation, Drosophila eye development, focusing on the activator-inhibitor system responsible for spacing the R8 photoreceptors that define the eye's regular ommatidial crystal. The R8 lattice grows by activating the expression of proneural genes at a moving front to create new columns of R8 cells. I propose a model where the dynamics of initial induction plays a central role in selecting the eventual R8s. Unlike in a textbook Turing instability picture, the final pattern is thus strongly history-dependent. In particular, transient perturbations of one column can change the pattern in all subsequent columns. Most strikingly, in certain circumstances the normal triangular lattice can give way to stripes of R8 cells. These predictions are confirmed experimentally by manipulation of the Notch and scabrous genes. Our model also provides insight into several previously puzzling observations; for example, it naturally explains why R8 cells normally appear at the posterior of proneural intermediate groups and why mosaic analysis defines the R8 cells as uniquely important for sca function, even though more sca is produced elsewhere in the IG's. In contrast to the standard proneural model, our picture implies that R8 cells are selected before the appearance of the full group of proneural cells. This prediction may have broader implications for the selection of neural cells by lateral inhibition; I will close by speculating on how it might be tested in flies mosaic for components of the Notch pathway.