Dr. David K. Lubensky
Department of Physics & Astronomy
Vrije Universiteit
Amsterdam

Monday, March 14, 2005
4:00 pm (CT)
464 Loomis

Abstract

Pattern formation has interested physicists at least since the work of Faraday and Oersted in the early nineteenth century [Faraday, 1831]; since then, regular patterns have been observed in systems ranging from sand dunes to lasers to spin waves [Cross and Hohenberg,1993]. Mixtures of reacting and diffusing chemicals hold a special place in this group, both because they were among the first to be studied from the point of view of nonequilibrium statistical physics [Nicolis and Prigogine, 1977] and because of longstanding interest in their relevance to biology [Meinhardt, 1992]. Only recently, however, have mechanisms of biological pattern formation been deciphered in enough detail to allow extensive comparisons between models and experiments. Here, we study one of the most remarkable examples of such pattern formation, the development of the fruit fly's compound eye. We propose that the pattern of cell fate in the fly's retina is generated primarily by a novel "epitaxial" process in which it is progressively built up row by row behind a moving front. A clear prediction of our model is that if the communication between successive rows is broken, even transiently, a striped pattern will appear instead of the usual triangular lattice; this phenomenon has indeed recently been observed in some mutants. Although inspired by developmental biology, our model also has more general implications. In particular, it shows that, contrary to conventional wisdom, the pattern selected by a moving front need not be unique. Our work I thus an example of how biological problems can inspire new perspectives on basic problems in theoretical physics.