Pentagone- and Dally-mediated regulation of Dpp signaling produces active scaling by an ER feedback mechanism. (A) Schematic showing expander-repressor regulation of modulator action on the morphogen Dpp. Expander corresponds to Dally and Pent that feeds back (red lines) to modify the reaction and transport properties of the morphogen Dpp, which subsequently represses the expander (blue line). (B) Predicted distribution of normalized Dpp-Tkv (BR) as a function of relative position in different size discs that range from 60 to 120 μm. Here, the expander-repressor motif correctly adjusts decay length to provide scale invariance during disc growth. Inset shows log scale. (C) Same as in B except all individual profiles are normalized to the amplitude in the 60-μm disc. (In B, each profile is normalized to itself, which leads to each having a maximum amplitude of 1.) The plot shows decreasing morphogen amplitude as a function of disc size and developmental time. Inset shows log scale. Parameters and equations are provided in Ben-Zvi et al. (Ben-Zvi et al., 2011). (D) Core feedback scaling network in the ‘size-sensor’ model (Inomata et al., 2013). Here, feedback from BMP signaling (blue line) works through the modulators (red lines) Sizzled and Xlr to enhance the function of Chordin, which sequesters extracellular BMPs (a negative regulation). The gray arrow shows the net impact of feedback from BMP signaling on Chordin. (E) Proposed behavior for Sizzled in relation to embryo size according to the ‘size-sensor’ model (Inomata et al., 2013).