Extended Data Fig. 2: Analysis of Dpp leakage and effects of growth on Dpp gradient profile.

a, Confocal images of GBP-Alexa555 labelling extracellular GFP-Dpp in a control extracellular staining (top) and following a chase of living discs for 7 h at 4 °C. b, Total GBP-Alexa555 fluorescence in the conditions in a. Two-tailed two sample t-test, p-value = 0.7787. n, number of biologically independent samples. Bars, s.e.m. c, d, Schemes of sGFP^Ptc-Wg, see reference³¹ (c) and sGFP^Dpp constructs (d). Sizes of fragments represented in the scheme do not correspond to the nucleotide sequences. e, Confocal images of sGFP^Dpp (top), phalloidin staining (middle) and merge (bottom). Left panels, orthogonal views; right panels, xy plane. f, Normalized average spatial profile of sGFP^Dpp fluorescence (green) compared to the normalized profiles of gradients with decay lengths λ=λ_Dpp; λ = 6L; λ = 3L and λ = 2L with λ_Dpp = 28.9 µm and L = 144.6, average posterior size of eGFP-Dpp^LOP third instar discs. g, Orthogonal views of confocal images of sGFP^Dpp fixed immediately after dissection (0 h) and following a chase of living discs for 1h at 25 °C and 4 °C. h, Total sGFP fluorescence in the conditions in g, normalized for each temperature to the value at t = 0 h. Two-tailed two sample t-test for unequal variances, p-values: 0.9792 (25 °C) and 0.7543 (4 °C). n, number of biologically independent samples. Bars, s.e.m. i, Effect of leakage on parameterization of Dpp transport rates. Average estimated parameters considering leakage rates k_L = 0s⁻¹; 0.00001 s⁻¹; 0.0005 s⁻¹ and 0.001 s⁻¹. Simulations represent 3.7 x 10⁶ randomly chosen parameter sets per condition. j, Stacked bar chart showing the relative contribution of the different modules to λ² (described in Fig. 1e,f) for conditions in i. n, sample size; bars, s.d. k, Long-term FRAP assay. Dynamics of fluorescence recovery in conventional FRAP for one hour (red) and long-term FRAP for ten hours (blue). Fluorescence recovery is normalized to the signal in the ROI before bleaching. Note that recovery of conventional FRAP overlays the dynamics of long-term FRAP at short time scales. Bars, s.e.m. l, n, Dynamics of long-term FRAP recovery and fit to double (l, blue line) and single exponential dynamics (n, blue line) to the dataset (both early and late). Box in l, late recovery (after 5,000 s) analysed in m. m, Dynamics of long-term FRAP recovery (late recovery) and single exponential fit (blue line) to the late slow dynamics. o, Wing disc area plotted as a function of disc age in staged larvae (hours after egg laying) and fit to an exponential growth in which growth rate decays exponentially over time (red line). See Supplementary Information section 2.9. Orange and blue lines correspond to area and age of discs of l = 144 µm and l = 80 µm posterior length, respectively, as determined by the plot in p. p, Posterior compartment length (l) as a function of wing disc area (A). Black line, power-law fit. Growth anisotropy \(m={g}_{x}/g=\frac{\dot{{\ell }}/{\ell }}{\dot{A}/A}\). Using m, the area of discs of l = 144 µm and l = 80 µm posterior length can be determined (orange and blue lines). q, Wing disc growth rate (g), relaxation rate of the slow dynamics (that of the immobile fraction, IF) in long-term FRAP (k_IF) and degradation rate of the immobile pool (k₂) estimated according to k₂ = k_IF − g. The timescales corresponding to these rates are indicated on top of bars. r, s, Measurement of the mobile pool decay length. r, Confocal images of eGFP-Dpp^LOP before (top) and at indicated times after bleaching (middle and bottom). s, Correlation between the decay length of the total pool of eGFP-Dpp at steady state (λ_T) measured before bleaching and the mobile pool decay length measured 30 min after bleaching (λ_M). Black line, linear regression. Note the slope close to 1, indicating that for discs of different sizes λ_M ≃ λ_T. Scale bar, 10 µm (a, e, g, r).

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