Two models of morphogen gradient formation

Dariusz Wrzosek
University of Warsaw

The process of cells differentiation is linked to the positional information which is specified by the local concentration of morphogen molecules (ligands). Morphogen is secreted in some restricted region by specialized cells. The transport of the morphogen molecules in an adjacent tissue and their interaction with cellular receptors lead to the formation of the gradient of morphogen concentration. Different hypotheses about the nature of the morphogen transport are investigated in the literature. We propose two different macroscopic models of morphogen transport which are derived from the kinetic level in one space dimension. The first model accounts for transcitosis i.e intracellular transport of bound receptors and the second one assumes receptor aided diffusive transport of ligands. In both cases we obtain quasilinear parabolic equation describing the transport of ligands coupled via diffusivity and reaction terms with an o.d.e describing bound receptors kinetics. This is a joint work with Piotr Krzyzanowski (University of Warsaw) and Philippe Laurençot (Université Toulouse III).