Scaling morphogen gradients during tissue growth by a cell division rule

Morphogen gradients guide the patterning of tissues and organs during the development of multicellular organisms. In many cases, morphogen signaling is also required for tissue growth. The consequences of this interplay between growth and patterning are not well understood. In the Drosophila wing imaginal disc, the morphogen Dpp guides patterning and is also required for tissue growth. In particular, it was recently reported that cell division in the disc correlates with the temporal increase in Dpp signaling. Here we mathematically model morphogen gradient formation in a growing tissue, accounting also for morphogen advection and dilution. Our analysis defines a new scaling mechanism, which we term the morphogen-dependent division rule (MDDR): when cell division depends on the temporal increase in morphogen signaling, the morphogen gradient scales with the growing tissue size, tissue growth becomes spatially uniform and the tissue naturally attains a finite size. This model is consistent with many properties of the wing disc. However, we find that the MDDR is not consistent with the phenotype of scaling-defective mutants, supporting the view that temporal increase in Dpp signaling is not the driver of cell division during late phases of disc development. More generally, our results show that local coupling of cell division with morphogen signaling can lead to gradient scaling and uniform growth even in the absence of global feedbacks. The MDDR scaling mechanism might be particularly beneficial during rapid proliferation, when global feedbacks are hard to implement.