Dynamic readout of the Hh gradient in the Drosophila wing disc reveals pattern-specific tradeoffs between robustness and precision

How patterning by morphogen gradients determine tradeoffs between robustness and precision is unclear. Gradients that exhibit self-enhanced ligand degradation provide robustness to perturbations in morphogen production rates. However, increased robustness achieved through this mechanism is traded off for lower precision to noise. Here we use a hypotheses-driven theoretical approach to show that Hedge-hog (Hh) signaling would confer the same robustness to all target genes established by the steady-state gradient, but when a dynamical interpretation of patterning is used, robustness is maintained for steady-state outputs, but is traded off for higher precision in outputs set prior to steady-state. As predicted by our model, the widths of decapentaplegic (dpp), and collier (col), two target genes established by the Hh gradient in the Drosophila wing disc, exhibit differential robustness to Hh dosage. Particularly, higher robustness in the col pattern is ensured by Hh-dependent upregulation of its receptor Patched, an evolutionary-conserved property of Hh signaling that results in self-promoted Hh degradation. In contrast, dpp expression that is determined by the transient overshoot gradient, is insensitive to self-enhanced ligand degradation and exhibits less robustness, in exchange for a more precise boundary. Our work reveals of how morphogen gradients can establish tunable patterning properties in a target-specific manner.