Dynamic scaling of morphogen gradients on growing domains.

Developmental mechanisms are highly conserved, yet act in embryos of very different sizes. How scaling is achieved has remained elusive. Here we identify a generally applicable mechanism for dynamic scaling on growing domains and show that it quantitatively agrees with data from the Drosophila wing imaginal disc. We show that for the measured parameter ranges, the Dpp gradient does not reach steady state during Drosophila wing development. We further show that both, pre-steady-state dynamics and advection of cell-bound ligand in a growing tissue can, in principle, enable scaling, even for non-uniform tissue growth. For the parameter values that have been established for the Dpp morphogen in the Drosophila wing imaginal disc, we show that scaling is mainly a result of the pre-steady-state dynamics. Pre-steady-state dynamics are pervasive in morphogen-controlled systems, thus making this a probable general mechanism for dynamic scaling of morphogen gradients in growing developmental systems.