Applied and Interdisciplinary Mathematics Seminar

University of Michigan

Winter 2007
Friday, 23 March, 3:10-4:00pm, 1084 East Hall

From neurocrystals to epitaxy: The developmental patterning of the fly's eye.

David K. Lubensky

University of Michigan


Abstract

Animals' ability to create the complex patterns found in many organisms is an enduring source of wonder and a topic that has long drawn the interest of scientists of all stripes. Here, we study one of the most striking and best-characterized examples of such pattern formation, the development of the fruit fly's compound eye. In the fly larva, a front of differentiation sweeps across the sheet of tissue that will become the adult retina. It leaves behind it a hexagonal array of cells marked by high levels of the protein Atonal. Building on recent progress in deciphering the basic genetic logic of this process, we propose the first model of retinal patterning based on experimentally verified interactions. Surprisingly, we conclude that the classic pattern formation mechanism based on a Turing instability cannot reproduce the observed behavior. Instead, we propose that the pattern is generated primarily by a novel "epitaxial" process in which, as the front progresses, each newly-created row of unit cells acts as a template for the next one. A clear prediction of this model is that if the communication between successive rows is broken, even transiently, a striped pattern will appear. Preliminary experimental tests suggest that this occurs in some mutants. Similar patterning processes have been observed in systems as diverse as feather buds and retinal ganglion cells; our model may thus describe an evolutionarily conserved module.