Cooperative Diffusion Leads to a Robust Morphogen Gradient

In many developmental systems, spatial patterns of cell and tissue organization arise from morphogen gradients, which assign cellular fates according to the different thresholds of morphogen concentrations. Typically, diffusion is regarded as a mechanism responsible for the formation of morphogen gradients. Previous studies presented two opposing diffusion mechanisms, namely receptor-mediated transcytosis (RMT) and restricted extracellular diffusion (RED), for explaining the range of morphogen gradients and their robustness, but the joint effect of intracellular and extracellular diffusions is unclear. Here, using partial differential equations, we model a morphogen dispersal mechanism including extracellular and intracellular diffusions. By introducing and analyzing a robustness index, we show that a properly cooperative diffusion can lead to a better robust morphogen gradient, in contrast to either RED or RMT alone. More precisely, there is an optimal cooperation of extracellular and intracellular diffusions such that the robustness and the range of morphogen gradients are optimal, respectively. Our results indicate that an appropriate cooperation between extracellular and intracellular diffusions is more beneficial to the robust formation of morphogen gradients than the simple diffusion proposed previously.