Understanding the principles underlying the design of robust, yet flexible patterning systems is a key problem in developmental biology. In the Drosophila wing, Hedgehog (Hh) signaling determines patterning outputs using dynamical properties of the Hh gradient. In particular, the pattern of collier (col) is established by the steady-state Hh gradient, whereas the pattern of decapentaplegic (dpp), is established by a transient gradient of Hh known as the Hh overshoot. Here, we use mathematical modeling to suggest that this dynamical interpretation of the Hh gradient results in specific robustness and precision properties. For instance, the location of the anterior border of col, which is subject to self-enhanced ligand degradation is more robustly specified than that of dpp to changes in morphogen dosage, and we provide experimental evidence of this prediction. However, the anterior border of dpp expression pattern, which is established by the overshoot gradient is much more precise to what would be expected by the steady-state gradient. Therefore, the dynamical interpretation of Hh signaling offers tradeoffs between robustness and precision to establish tunable patterning properties in a target-specific manner.

Hypothalamic kisspeptin (Kiss1) neurons are vital for pubertal development and reproduction. Arcuate nucleus Kiss1 (Kiss1^ARH) neurons are responsible for the pulsatile release of gonadotropin-releasing hormone (GnRH). In females, the behavior of Kiss1^ARH neurons, expressing Kiss1, neurokinin B (NKB), and dynorphin (Dyn), varies throughout the ovarian cycle. Studies indicate that 17β-estradiol (E2) reduces peptide expression but increases Slc17a6 (Vglut2) mRNA and glutamate neurotransmission in these neurons, suggesting a shift from peptidergic to glutamatergic signaling. To investigate this shift, we combined transcriptomics, electrophysiology, and mathematical modeling. Our results demonstrate that E2 treatment upregulates the mRNA expression of voltage-activated calcium channels, elevating the whole-cell calcium current that contributes to high-frequency burst firing. Additionally, E2 treatment decreased the mRNA levels of canonical transient receptor potential (TPRC) 5 and G protein-coupled K⁺ (GIRK) channels. When Trpc5 channels in Kiss1^ARH neurons were deleted using CRISPR/SaCas9, the slow excitatory postsynaptic potential was eliminated. Our data enabled us to formulate a biophysically realistic mathematical model of Kiss1^ARH neurons, suggesting that E2 modifies ionic conductances in these neurons, enabling the transition from high-frequency synchronous firing through NKB-driven activation of TRPC5 channels to a short bursting mode facilitating glutamate release. In a low E2 milieu, synchronous firing of Kiss1^ARH neurons drives pulsatile release of GnRH, while the transition to burst firing with high, preovulatory levels of E2 would facilitate the GnRH surge through its glutamatergic synaptic connection to preoptic Kiss1 neurons.