Position-dependent feedback drives scaling and robustness of morphogen gradients

Developmental patterning is remarkably robust to intrinsic and extrinsic variation. Morphogen gradients are a key mechanism driving patterning, and themselves often scale with the size of developing tissues and exhibit robustness to other perturbations. Recent data indicate that expander molecules, thought to drive morphogen scaling through expansion-repression (ER) feedback, have concentration profiles that are position dependent. This challenges the currently accepted ER mechanism that requires uniform expander concentrations and position independent feedback. To reconcile these observations, we introduce an ER motif that supports morphogen scaling with both uniform and position-dependent expander concentrations. We quantify scaling as a function of position, and demonstrate that the spatial profiles of scaling and robustness to perturbations in morphogen production are highly correlated. In contrast to uniform expander concentrations that can confer high levels of scaling and robustness at a single position, position-dependent expander concentrations can enhance both scaling and robustness throughout the entire target tissue. We explore trade-offs associated with the dynamic range of the expander concentration, revealing that it can be varied to tune the locations where morphogen gradients confer scaling, robustness, and precision simultaneously. These findings offer insight into how developmental systems balance competing demands to achieve reproducible patterning despite biological variability.