Hh signalling and R differentiation wave. (A) Confocal image of the ocellar region of a Hh:GFP; GMR>tdTomato (‘GMR>tom’) larva (stage 17 ommatidia), stained for Hh:GFP (blue), Ptc (green) and anti-Tomato (red). No R cells (‘GMR>tom’) have as yet differentiated. (A′) Quantitative profiles of the Hh:GFP, Ptc and GMR signals across the Hh-producing domain (shaded in grey) and the pOC (measured in the dashed yellow box in A). Hh:GFP signal decays non-linearly. Ptc signal follows that of Hh:GFP at this stage, when no R cell (GMR>Tom) has yet differentiated. (B,C) pOC regions (boxed, like the corresponding region in A) stained for Elav (blue) and Sens (red) of discs from larvae of the same stage (21 ommatidia). In the control (B, ‘eyaL>+’) a row of R-expressing Elav cells precedes a row of Sens-expressing precursors. In eyaL>Ci-PKA (C, causing the uniform expression of Ci), precocious differentiation is observed. In addition, the differentiation wave, characterized by the succession Elav→Sens, is broken. (D) Number of Elav-positive cells in the pOC (red) and aOC (green) as a function of developmental time. The number of ommatidial rows in the compound eye, which increases linearly with time, was used as an internal developmental timer. Individual data points (circles) and the means are represented and fit well to a line. See Materials and Methods for a description of the statistical analysis.

Altering Hh spatial distribution distorts the differentiation wave. (A,B) Cartoon depiction of the Hh sources (green domains) relative to the retina-competent regions (blue) in control (A) and wg>Hh (B) ocellar regions. The posterior ocellus is marked as ‘pOC’. The green triangles indicate the distribution of Hh from these sources. In wg>Hh, Hh is expressed around the ocelli and within the normal Hh expression domain. (C) Late wg>Hh disc (stage 23) stained for GFP (GFP:Hh), Sens and Elav. The boxed region corresponds to that represented in A and B. A′ and B′ are pOC regions from control and wg>Hh individuals, respectively. (D,D′) Ocelli of control (D) and wg>Hh (D′) adults. In wg>Hh, ocelli are larger.

Loss of Ptc in R cells suffices to explain linear differentiation dynamics. (A) Cartoon diagram of the model for the Hh signalling pathway and its downstream effects. (B,E) Spatio-temporal dynamics of the outputs of the model without considering (B) or considering (E) a negative feedback from Elav-expressing R cells to Ptc (‘E’ link in A). (B) R cells (blue) accumulate hyperbolically and do not reach the end of the competent region within the time frame of 50 h. (E) With negative feedback (all other parameters are the same), R accumulation dynamics are close to linear and R differentiation reaches the end of the competent region. Simulations have been carried out, including a 50% reduction in Hh production rate along the 50 h time, as observed experimentally. Similar results are obtained if this rate is constant (Fig. S5). (C,D) Ocellar region of stage 18 (C,C′) and stage 23 (D,D′) eyaL>GFP discs stained for GFP (marking the Eya-expressing competence domain), Ptc and Elav (R cells). Axes are as in Fig. 1. Elav-expressing cells (marked by arrows) show reduced levels of Ptc. Source code is available in the supplementary material under source code File 1.

Robustness in the dynamics of the wave against changes in Hh increases when Ptc feedback is present. (A,B) Space-time plots when Hh concentration is increased and decreased by 10% compared in the absence (A) or presence (B) of Ptc reduction in R cells. Colours represent the expression levels of Ptc (green), Sens (red) and Elav (blue). The solid line is used to represent the speed of the wave as a guide to the eye. The intensity of Hh in the left panel in A has been adjusted to facilitate comparison between A and B. (C) Changes in the dynamics of the wave due to changes in Hh concentration. The model with no Ptc reduction (blue dashed line) is more sensitive to changes in Hh concentration than the situation with Ptc reduction. Statistics performed using 30 independent simulations for each point. Bars indicate the s.d. of each measurement. (D) Schematic depiction of the model proposed. Hh spreading leads to Ptc upregulation and maximal signal initially closest to the source. As the cells differentiate, Ptc levels decrease, allowing farther extension of Hh spreading. By each cell dynamically responding to Hh, the ocellar primordium transforms a noisy non-linearly decaying signal into a differentiation wave of constant speed that is robust to signal noise. Source code for Hh signalling model available in the supplementary material under source code File 1.