MATHEMATICAL MODELS OF RECEPTOR-MEDIATED TRANSPORT OF MORPHOGENS

Two models of receptor-mediated morphogen transport in a biological tissue are proposed to investigate morphogen gradient formation. The first model concerns intracellular transport of morphogen molecules, while the second describes transport along the cell surface. Both models couple via diffusivity a quasilinear degenerate parabolic equation describing the transport of the morphogens with an ordinary differential equation describing reversible binding kinetics of receptors. A detailed study of the steady states is provided, together with numerical tests which compare the models with experimental data.