  We present a general theoretical framework to discuss mechanisms of morphogen
transport and gradient formation in a cell layer. Trafficking events on the
cellular scale lead to transport on larger scales. We discuss in particular the
case of transcytosis where morphogens undergo repeated rounds of
internalization into cells and recycling. Based on a description on the
cellular scale, we derive effective nonlinear transport equations in one and
two dimensions which are valid on larger scales. We derive analytic expressions
for the concentration dependence of the effective diffusion coefficient and the
effective degradation rate. We discuss the effects of a directional bias on
morphogen transport and those of the coupling of the morphogen and receptor
kinetics. Furthermore, we discuss general properties of cellular transport
processes such as the robustness of gradients and relate our results to recent
experiments on the morphogen Decapentaplegic (Dpp) that acts in the fruit fly
Drosophila.
