Diffusion, Reaction, and Biological pattern formation

Leah Edelstein-Keshet
Mon, May 14, 2012
PIMS, University of British Columbia
Mathematical Cell Biology Summer Course
We first consider the topic of biological patterns and then place it in the context of developmental biology and positional information. The example of the fruit fly (Drosophilla) development is used to motivate the basic questions. We next consider how chemical interaction coupled to diffusion can give rise to pattern formation. We discuss Turing's (1952) theory for pattern formation and derive the conditions for this to happen in a system of two interacting chemicals. Returning to the fruit-fly example, we observe that the mechanism for development (based on reading the level of bicoid protein) has been shown to be distinct from a Turing pattern