The underlying mechanisms that generate shapes and patterns in biology are characterized by a remarkable robustness, despite the uncontrollable parameter variability. More than half a century ago, Alan Turing published a landmark mathematical study entitled “The Chemical Basis of Morphogenesis” to explain how patterns in biology could be produced via certain classes of reaction-diffusion systems.
This mathematical theory proposed the novel idea that two homogeneously dispersed “morphogens” - chemicals that determine a cell’s fate or characteristics - can autonomously generate spatial patterns such as stripes and spots. Turing’s work is considered a masterpiece of mathematical modeling, and has gained acceptance as a prototype model of pattern formation among theoretical biologists. However, it is now becoming evident that the Turing model does not always capture biological reality.
Indeed, over the past several years, active transport mechanisms – distinct from the Turing mechanism – have been shown to play a surprising and previously unrecognized role in patterning and development, and which may hold the key to the remarkable robustness of biological patterning.
An Honours or MPhil project would undertake a thorough analysis of both the Turing mechanism and the recent active transport (shuttling) mechanism proposed by the Ben-Zvi/Barkai morphogen model for the amphibian embryo. An MPhil project would also develop a novel mathematical model of the active transport mechanism recently discovered in Zebrafish stripe patterning, where macrophages (a special type of immune cell) play an active role in organizing pigmented cells into stripes. Both project formats (Honours or MPhil) would be suited to further continuation as a PhD project if the student is interested. The project could also be started at PhD level.
This project has the potential to make an important contribution to our understanding of the deeply mathematical mechanisms that govern life’s blueprint.
Skills and experience
- MXB201 (or equivalent)
- MXB221 (or equivalent)
- MXB322 (or equivalent)
- MXB323 (or equivalent)
You may be able to apply for a research scholarship in our annual scholarship round.
- Reaction-diffusion equations
- Turing mechanism
- Biological patterning
- Morphogen profiles
- Partial differential equations
Contact the supervisor for more information.