Spatio-temporal patterns with piecewise-linear regulatory networks

Project description

A number of fascinating and important biological processes involve various kinds of spatial patterns: spatial patterns on animal skins, orthe very regular organ arrangements found in plants (called phyllotaxis) for instance. These patterns often originate at very small scales, and their onset can only be seen using very recent microscope and image analysis techniques. Among several families of models for biological patterning, one of the simplest is based on the idea that mobile substances (called morphogens) are acting upstream of their targets, which respond locally to a globally defined gradient pattern. In this project one will consider models where targets are themselves mobile morphogens, potentially regulating their own input. One will study the effect of such spatial feedback on patterning. To do so, one will rely on a class of models which are biologically relevant, tractable analytically, and not much studied yet in a context with spatial interactions. A class of models which meet all this criteria is provided by piecewise-linear differential equations.