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.