Extended Data Fig. 3: Parameterization assay controls I: steady-state decay length and nanobody internalization.

a, Immunoprecipitation of eGFP-Dpp under different expression systems. See Methods. Input (I) and immunoprecipitate (IP) from eGFP-Dpp^CRISPR/+ (lanes 1,2), eGFP-Dpp^CRISPR/CyO,Dpp⁺ (lanes 3,4), dppLG/+ ; LOP-eGFP-Dpp/+ (lanes 5,6; eGFP-Dpp^LOP) and Dpp-Gal4/UAS- sfGFP-mKate2-Dpp larval head extracts (lanes 7,8). Mature GFP-Dpp fragment after Furin cleavages is marked by an asterisk. Note that GFP-Dpp amounts when expressed using LexA/LOP system are similar to the amounts of GFP-Dpp endogenously expressed (1.1 fold), whereas Gal4/UAS system expresses almost 400 fold more GFP-Dpp. For gel source data, see Supplementary Fig. 1b. b, Confocal image of eGFP-Dpp^LOP in the background of overexpression of Dpp by dppGal4. c, d, Dynamics of FRAP recovery (c) and nanobody uptake (d) in this condition (red lines) as compared to control (blue).Bars, s.e.m. e, Average decay length λ of the gradients considered in the three datasets, corresponding to the three conditions considered in this report: large discs (average posterior length l = 144 µm in the dataset), small discs (average l = 80 µm) and in a pent² mutant disc (average l = 130 µm). Bars, standard error to the mean (s.e.m.). The average decay length for the average l corresponding to the three experimental conditions was estimated using the linear regression of eGFP-Dpp^LOP control (sample size n = 157 discs) and pentagone mutant (n = 63 discs) datasets (see Fig. 2a). f, Confocal images (maximum projections) of the eGFP-Dpp^LOP gradient (red box, region of interest (ROI) in the posterior compartment) in representative discs from the three conditions described in b. The source is to the left. g, Average spatial distribution of eGFP-Dpp^LOP in these datasets. Shaded areas, s.e.m. Black line, exponential fit. h, i, Left, normalized eGFP-Dpp^LOP profiles in large control discs (h; l = 144 µm) and pent² mutant disc (i; l = 130 µm); right, average residuals of the fits of these profiles to an exponential function. Bars, s.e.m. j, Scaling plot of eGFP-Dpp^LOP. Decay length (λ, from the exponential fit) of the eGFP-Dpp^LOP gradient versus l. Red line, linear regression. ϕ_L = λ/l determined from the linear regression. k, GBP-Alexa555 signal intensity as a function of time in 13 different discs. Lines, fits to the phenomenological \({c}_{{\rm{T}}}^{i}(t)\,\)equation for the internalized signal intensity (left equation in m; red/green boxes as in l). l, Average dynamics of the GBP-Alexa555 fluorescence signal in the three conditions. Bars, s.e.m. m, Parameterization of k_N, k_o and k_r based on the dynamics of GBP-Alexa555 signal. Left, phenomenological \({c}_{{\rm{T}}}^{i}(t)\,\)equation which captures the exponential (red box; see also l) and linear dynamics (green box) of the accumulation of the GBP-Alexa555 signal. Right, relationship between the phenomenological parameters A, B and p and k_N, k_o and k_r (see Supplementary Information section 2.2.1). n, Scheme of the GBP-Alexa555 internalization assay. Rates and pools indicated, like in Fig. 1d. Note that the fluorophore (Alexa555; star) degrades on a time scale which is much longer than the duration of the experiment. o, Confocal images of internalized GBP-Alexa555 in a disc expressing eGFP-Dpp^LOP (top) and a control disc (bottom) at indicated timepoints of nanobody internalization using the same nanobody concentration as in Fig. 2b–f. Note that, under these conditions, fluid-phase internalization of the nanobody in the absence of eGFP-Dpp^LOP (bottom, control) is negligible compared to the internalization when bound to eGFP-Dpp^LOP (top, eGFP-Dpp). p, Dynamics of internalized GBP-Alexa555 in the disc expressing eGFP-Dpp^LOP (green curve) and a control disc (blue curve), in the same experimental conditions (e.g. same nanobody concentration) as in the nanobody uptake experiments in o. Note that, in these conditions, internalization of GBP-Alexa555 by fluid phase in the absence of GFP-Dpp is negligible. q–r, Dynamics of fluid-phase internalization of GBP-Alexa555. q, Confocal image of fluid-phase internalized GBP-Alexa555 (40 min of nanobody incubation) showing that, at high concentration of the nanobody, a signal can be detected at low levels which is homogenous in space (there is no gradient). Five-fold higher concentration of the nanobody than in o was used to reliably detect the signal of the fluid-phase internalized nanobody. r, Dynamics of fluid-phase internalized GBP-Alexa555 signal intensity, averaged over 3 independent experiments. Same concentration as in p. Shaded area, s.e.m. Note that the dynamics do not show the early exponential regime seen in the presence of eGFP-Dpp, indicating that the nanobody by itself is not significantly recycled. s, Top, confocal image of fluid-phase internalized Alexa555 (40 min of Alexa555 incubation). Also here, internalization of the fluorophore is homogeneous in space. Bottom, high magnification of the ROI area shown in the top. t, Dynamics of fluid-phase internalized Alexa555, showing a linear increase without saturation in the timescale of the experiment, which reflects a lack of degradation in the lysosome of the Alexa555 fluorophore. u, Confocal images of the eGFP-Dpp^LOP gradient (left) and internalized GBP-Alexa555 (right) after 45 min of incubation with the nanobody in a control large disc. The source is to the left. In contrast to the situation for fluid phase internalization (p, r), internalized eGFP-Dpp^LOP with GBP-Alexa555 is distributed as a gradient. v, Spatial profiles of the gradients in u in the posterior compartment. The decay length is determined by fitting the spatial profiles to an exponential function with an offset. The decay length is given with its confidence interval. n, number of biologically independent samples. Bars, s.e.m (c, g, h, l, r). Scale bars, 10 µm (b, f, o, s, u) and 50 µm, (q).

Source data