Abstract
Morphogen gradients are fundamental to establish morphological patterns in developing tissues^{1}. During development, gradients scale to remain proportional to the size of growing organs^{2,3}. Scaling is a universal gear that adjusts patterns to size in living organisms^{3,4,5,6,7,8}, but its mechanisms remain unclear. Here, focusing on the Decapentaplegic (Dpp) gradient in the Drosophila wing disc, we uncover a cell biological basis behind scaling. From small to large discs, scaling of the Dpp gradient is achieved by increasing the contribution of the internalized Dpp molecules to Dpp transport: to expand the gradient, endocytosed molecules are reexocytosed to spread extracellularly. To regulate the contribution of endocytosed Dpp to the spreading extracellular pool during tissue growth, it is the Dpp binding rates that are progressively modulated by the extracellular factor Pentagone, which drives scaling. Thus, for some morphogens, evolution may act on endocytic trafficking to regulate the range of the gradient and its scaling, which could allow the adaptation of shape and pattern to different sizes of organs in different species.
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Data availability
Source data are provided with this paper. Datasets generated during the parameter estimation are available in GitHub (https://github.com/zenah12/DppTrafficking/blob/main/README.md). Source data are provided with this paper.
Code availability
Source codes are available in GitHub (https://github.com/zenah12/DppTrafficking/blob/main/README.md). MATLAB code corresponding to the binning of control and pent mutant data in Fig. 2a is available upon request.
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Acknowledgements
We thank R. Mateus and I. Castanon Ortega for their feedback on the manuscript; F. Karch for Cre recombinase; K. Basler for the stock to make brk^{M68} tkv^{8} mutant clones; E. Doná for the p744_p3E_mkate2sfGFP plasmid; M. Affolter for the LexA inducible eGFP::DPP; K. Kruse for discussions; E. Derivery for the purified sfGFPmKate2; V. RasulKareeva for various contributions; and the Bioimaging Center of University of Geneva for microscopy support. Z.H. was supported by an HFSP longterm fellowship; and M.G.G. was supported by the DIP of the Canton of Geneva, SNSF, the SystemsX EpiPhysX grant, the ERC (Sara and Morphogen) and the NCCR Chemical Biology program.
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Contributions
M.R.M. performed most experiments and quantifications and performed data analysis. D.A.H., Z.H. and F.J. developed the theory and performed data analysis. Z.H. and D.A.H. performed numerical simulations. C.S. cloned and made fly stocks to express Dpp^{Timer} and UAS Pentagone::GFP, performed immunoprecipitations and purified the GBP. D.B. performed the photoconversion experiment, labelled the purified GBP with Alexa555, cloned and purified GBP–Dendra2 and developed the acid wash. M.D. made the Dpp^{CRISPR} stock. M.R.M. and M.G.G. conceived and designed experiments. M.R.M. and Z.H. prepared figures. M.R.M., Z.H., F.J. and M.G.G. prepared the manuscript.
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Extended data figures and tables
Extended Data Fig. 1 Photoconversion assay controls and two extreme regimes of Dpp transport.
a–d, Photoconversion assay. Test of efficiency of the acid wash in the photoconversion experiment using GBPDendra2: GFPDpp expressing discs have been incubated in GBPDendra2 for 50 min at 4 °C (the nanobody is only bound to the extracellular pool) and subsequently acidwashed to remove the label of the extracellular pool. Confocal image of eGFPDpp^{LOP} expressing disc (a) and corresponding images of Dendra2* (b) before photoconversion (left) and 40 min following photoconversion (right; see Materials and Methods). Note that no detectable Dendra2* signal is observed 40 min after the acid wash, indicating that the extracellular pool of nanobodies has been efficiently removed and that the potential extracellular leftover (below the detection limit) cannot lead to an observable recovery in intracellular compartments. c, Comparison between eGFPDpp^{Gal4} gradient profiles and gradient profiles formed by photoconverted Dendra2* propagated into the posterior compartment of the discs (photoconversion experiments as in Fig. 1a). Bar plot showing ϕ=λ/l of eGFPDpp^{Gal4} gradient profiles and photoconverted Dendra2* gradient profiles for large discs. Bars, standard deviations. Twotailed two sample ttest, pvalue = 0.2353. d, Fluorescence intensity of Dendra2* in a ROI of 6x35 µm at the source boundary in the photoconversion experiment in Fig. 1a. Measured Dendra2* fluorescence (blue dots) is plotted as a function of time after the photoconversion event. The red line represents the theoretical dynamics of Dendra2* fluorescence signal considering the parameterized values for large discs. n = 4 biologically independent samples. Data represented as mean values ± s.e.m. e–h, Acid wash efficiently removes the extracellular pool. Confocal images of eGFPDpp^{LOP} gradient (green in e, f), and extracellular eGFPDpp^{LOP} pools monitored by means of an extracellular immunostaining (see Materials and Methods, Supplementary Information section 2.3.2) by using a GBPAlexa555 nanobody against GFP (g, h; red in e, f) before (e, g) and after (f, h) acid wash. Acid wash in these conditions largely reduces the extracellular staining down to 9% of the signal. Scale bar: 10 µm. i, Acid wash does not affect internalized GBPAlexa555. Confocal images of eGFPDpp^{LOP} (top, green) and GBPAlexa555 internalized for 40 min (bottom, red) before (left) and after acid wash (right). The GBPAlexa555 signal decreases by 2.3 ± 0.6% after acid wash. j, Acid wash: effect of pH on GBP binding to GFP from larval extracts. Immunoblot of GFP which was bound to GFPTrap beads (Chromotek, GFPTrap beads, lanes 37) and GFP dissociated from GFPTrap beads (supernatant, lanes 812) following treatment at different pH. FT, flowthrough (lane 1), PD, pulldown (lane 2). For gel source data, see Supplementary Fig. 1a. k, Stacked bar chart showing the relative contribution of the different modules to Dpp transport in the two theoretical extreme regimes of morphogen transport: extracellular diffusion (ExD^{20}) and transcytosis (Tr) regimes. The relative contribution of different modules is expressed as the ratio λ_{i}^{2}/λ^{2} with the index i corresponding to each of the four modules (i = u,b,r,t). Note that the unbound module contributes almost exclusively to λ^{2} in ExD and the transcytosis module, in Tr. l, Theoretical values of the 8 transport rates characteristic for ExD (rate values as in reference^{20}) and Tr regimes of morphogen transport. m, n, FRAP recovery with respect to the two extreme theoretical regimes. Red lines, calculated recovery curves in a FRAP experiment for a set of parameter values corresponding to the extreme Tr (m) and ExD^{17} regimes (n). Blue dots, average of the experimental recovery curves in discs of l = 144 µm average posterior length. n = 9 biologically independent samples. Data represented as mean values ± s.e.m. The coefficient of determination R^{2} characterizes how well the calculated curves fit the experimental FRAP data. λ, decay length of the Dpp gradient profile calculated using equation (1) and the set of parameter values corresponding to Tr and ExD (see Supplementary Information section 4.2). Bars, s.e.m. Scale bar, 10 µm (a, h, i).
Extended Data Fig. 2 Analysis of Dpp leakage and effects of growth on Dpp gradient profile.
a, Confocal images of GBPAlexa555 labelling extracellular GFPDpp in a control extracellular staining (top) and following a chase of living discs for 7 h at 4 °C. b, Total GBPAlexa555 fluorescence in the conditions in a. Twotailed two sample ttest, pvalue = 0.7787. n, number of biologically independent samples. Bars, s.e.m. c, d, Schemes of sGFP^{PtcWg}, see reference^{31} (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 eGFPDpp^{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. Twotailed two sample ttest for unequal variances, pvalues: 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 10^{6} randomly chosen parameter sets per condition. j, Stacked bar chart showing the relative contribution of the different modules to λ^{2} (described in Fig. 1e,f) for conditions in i. n, sample size; bars, s.d. k, Longterm FRAP assay. Dynamics of fluorescence recovery in conventional FRAP for one hour (red) and longterm 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 longterm FRAP at short time scales. Bars, s.e.m. l, n, Dynamics of longterm 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 longterm 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, powerlaw 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 longterm FRAP (k_{IF}) and degradation rate of the immobile pool (k_{2}) estimated according to k_{2} = 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 eGFPDpp^{LOP} before (top) and at indicated times after bleaching (middle and bottom). s, Correlation between the decay length of the total pool of eGFPDpp 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).
Extended Data Fig. 3 Parameterization assay controls I: steadystate decay length and nanobody internalization.
a, Immunoprecipitation of eGFPDpp under different expression systems. See Methods. Input (I) and immunoprecipitate (IP) from eGFPDpp^{CRISPR}/+ (lanes 1,2), eGFPDpp^{CRISPR}/CyO,Dpp^{+} (lanes 3,4), dppLG/+ ; LOPeGFPDpp/+ (lanes 5,6; eGFPDpp^{LOP}) and DppGal4/UAS sfGFPmKate2Dpp larval head extracts (lanes 7,8). Mature GFPDpp fragment after Furin cleavages is marked by an asterisk. Note that GFPDpp amounts when expressed using LexA/LOP system are similar to the amounts of GFPDpp endogenously expressed (1.1 fold), whereas Gal4/UAS system expresses almost 400 fold more GFPDpp. For gel source data, see Supplementary Fig. 1b. b, Confocal image of eGFPDpp^{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 pent^{2} 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 eGFPDpp^{LOP} control (sample size n = 157 discs) and pentagone mutant (n = 63 discs) datasets (see Fig. 2a). f, Confocal images (maximum projections) of the eGFPDpp^{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 eGFPDpp^{LOP} in these datasets. Shaded areas, s.e.m. Black line, exponential fit. h, i, Left, normalized eGFPDpp^{LOP} profiles in large control discs (h; l = 144 µm) and pent^{2} 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 eGFPDpp^{LOP}. Decay length (λ, from the exponential fit) of the eGFPDpp^{LOP} gradient versus l. Red line, linear regression. ϕ_{L} = λ/l determined from the linear regression. k, GBPAlexa555 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 GBPAlexa555 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 GBPAlexa555 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 GBPAlexa555 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 GBPAlexa555 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 GBPAlexa555 in a disc expressing eGFPDpp^{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, fluidphase internalization of the nanobody in the absence of eGFPDpp^{LOP} (bottom, control) is negligible compared to the internalization when bound to eGFPDpp^{LOP} (top, eGFPDpp). p, Dynamics of internalized GBPAlexa555 in the disc expressing eGFPDpp^{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 GBPAlexa555 by fluid phase in the absence of GFPDpp is negligible. q–r, Dynamics of fluidphase internalization of GBPAlexa555. q, Confocal image of fluidphase internalized GBPAlexa555 (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). Fivefold higher concentration of the nanobody than in o was used to reliably detect the signal of the fluidphase internalized nanobody. r, Dynamics of fluidphase internalized GBPAlexa555 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 eGFPDpp, indicating that the nanobody by itself is not significantly recycled. s, Top, confocal image of fluidphase 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 fluidphase 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 eGFPDpp^{LOP} gradient (left) and internalized GBPAlexa555 (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 eGFPDpp^{LOP} with GBPAlexa555 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).
Extended Data Fig. 4 Parameterization assay controls II: FRAP, extracellular fraction determination and parameter estimation by ABC.
a, Left, confocal image of the eGFPDpp^{LOP} gradient in a FRAP experiment (source and posterior compartment). Red box, region to be photobleached. Right, eGFPDpp^{LOP} fluorescent signal in the red box region before photobleaching (−1 min) and at different times (as indicated below) after photobleaching. b, Average dynamics of fluorescence recovery in the bleached area in the three experimental conditions (discs of l = 144 µm and l = 80 µm posterior length and in a pent^{2} mutant disc). Data represented as mean values. Bars, s.e.m. Lines, calculated recovery using the fivepool theoretical framework for a set of parameter values. The coefficient of determination R^{2} characterizes how well the theoretical curves fit the FRAP data. n, sample size. c, d, Robustness analysis of the FRAP assay. The average FRAP trace was fitted by a single dynamic equation^{3}. Dependence of the goodness of the fit (R^{2}) to this single dynamic equation (c) and the effective diffusivity (D_{eff}) estimated by this fit (d) on the number of individual recovery curves (n) considered for the average FRAP trace. The analysis was performed for the three experimental conditions of this report: large discs (average posterior length l = 144 µm in the dataset; left), small discs (average l = 80 µm; centre) and pent^{2} discs (right). Bars, confidence intervals (d). In d data are represented as D_{eff} estimated by fit for varying number of independent recovery curves, n. Bars, confidence intervals of fit. e, Effective diffusivity (D_{eff}, left) and effective degradation rate (k_{eff}, right) plotted against the average posterior length of discs within two datasets: small (average l = 80 µm) and large (average l = 144 µm). The average FRAP recovery curve was fitted by a single dynamic equation^{3} to determine D_{eff} and k_{eff}. Note, that as discs grow, D_{eff} does not change significantly, whereas k_{eff} decreases significantly, as previously reported^{23}. Data is represented as D_{eff} and k_{eff} estimated by fit. Bars, confidence intervals of fit. n, number of biologically independent samples. Onetailed two sample ttest with unequal variances; pvalues: 0.1765 (D_{eff}, left) and 0.0038 (k_{eff}, right). f, Simulated intensity profile of eGFPDpp^{LOP} at indicated times after photobleaching in the ROI in the posterior compartment (experiment as in a). x, distance from the edge of the anterior compartment. Parameter values used in the simulations are those of our parmeterization for l = 144 µm. g, Confocal images of the eGFPDpp^{LOP} gradient (left; total pool), and the extracellular eGFPDpp^{LOP} pools monitored by means of an extracellular immunostaining (see Supplementary Information section 2.3) by using a GBPAlexa555 nanobody against GFP (right; extracellular pool). Higher magnification of the fluorescent signal of the area boxed in the images are shown to the right. h, Expression of the extracellular fraction (ρ) as function of Dpp transport rates. i, Equimolarity of the GBPAlexa555 and eGFP solutions used for calibration of the Alexa555 versus GFP fluorescent signal (see Methods, Supplementary Information section 2.3.2; relevant to the extracellular fraction determination assay). The concentrations of GBPAlexa555 and eGFP was first roughly determined by means of a BCA assay (Supplementary Information section 2.3.2). Plot of GFP fluorescence intensity as a function of the ratio of GBPAlexa555 and GFP concentrations (determined by BCA) in the solutions. The relative concentration of GFP and GBPAlexa555 can be determined from the relative concentration at which the minimum value (r_{min}) of GFP fluorescence has been reached. Note that r_{min} ≃ 1 confirms that the BCA estimation was already accurate. j, Parameter value sets determined by the parameterization procedure (see Supplementary Information section 2.5.2) are represented in the (k_{on}, k_{off}) plane. Light orange area represents the full space of 3 × 10^{7} parameter value sets considered (l = 144 µm dataset). Dark orange dots represent sets of parameter values within those which satisfy the constraints given by the steadystate decay length, the longterm FRAP assay, the nanobody internalization and the FRAP assay. Calculated FRAP recovery curves using these sets of values fit the experimental FRAP data with R^{2}>0.92. Note that the solutions are separated into two clusters (clouds): the upper cloud, with higher k_{on}, k_{off}, is characterized by a low extracellular fraction ρ<0.10 and a lower cloud, by a high ρ<0.25. k, Selected sets of parameter values from j for which the calculated extracellular fraction is within the experimentally determined range of ρ values (0.08<ρ<0.18). l, Sets of parameter values which satisfy all the constraints given by our assays (see Supplementary Information section 2.5.2), represented in (k_{off}, k_{on}), (k_{off}, k), (D_{0}, k_{on}) and (k_{o}, k_{on}) planes. The parameter values corresponding to the two extreme theoretical cases discussed in Supplementary Information section 4.2 (Extracellular diffusion regime, ExD, yellow and Transcytosis regime, Tr, purple) are represented by circles for comparison. m, Average estimated parameters in the three experimental conditions compared to the theoretical values of parameters in ExD and Tr. Bars, s.d. N, number of parameterized sets of values. Scale bars: 10 µm (a, g).
Extended Data Fig. 5 Quantitative considerations: robustness analysis and decay length boosts.
a, Cluster of parameter value sets in the (k_{on}, k_{off}) plane corresponding to three different ranges of R^{2} to the experimental FRAP recovery for the three experimental conditions. The coefficient of determination R^{2} characterizes the goodness of the fit between the FRAP data and the calculated recovery curves. Relaxing the quality of fit down to R^{2}>0.85 (from R^{2}>0.93) does not populate the lower cloud, and therefore does not affect the assignment to the ExDtype versus Combined transport regimes. Points that populate the lower cloud as in the l = 80 µm and pent^{2} conditions) require that R^{2}< \({{\rm{R}}}_{{\rm{th}}}^{2}\) (see Supplementary Information section 3.7 for details). b, Cluster of parameter value sets in the (k_{on}, k_{off}) plane corresponding to different ranges of calculated extracellular fraction ρ for the three experimental conditions. An increase in ρ beyond ρ^{*} is required to shift the solutions to the “lower” cloud. The lower cloud is characteristic of the ExDtype regime. c, d, Sets of parameter values (clouds of points) compatible with all the assays considered in this report in the (k_{on}, k_{off}) plane. Isolines for Boost k_{r} (c) and Boost k_{off} (d) are also represented (see look up table). See Supplementary Information section 3.5 for definition of the Boosts. The three conditions considered in this work are shown: large discs (average posterior length l = 144 µm in the dataset; left), small discs (average l = 80 µm; centre) and pent^{2} discs (right). e, Average calculated Boost k_{r}, Boost k_{off} and Boost D_{0} for the three experimental conditions compared to the calculated Boosts for the theoretical values of parameters in the ExD and Tr regimes. N, number of parameterized sets of values. Data represented as mean values over N parameterized value sets. Bars, s.e.m. f–i, iFRAP assay. f, Scheme of the iFRAP assay (see Supplementary Information section 2.7). g, h, Test of efficiency of the acid wash in the iFRAP (and photoconversion) experiment: GFPDpp expressing discs have been incubated in GBPAlexa555 for 50 min at 4 °C (the nanobody is only bound to the extracellular pool) and subsequently acidwashed to remove the label of the extracellular pool. Confocal image of eGFPDpp^{LOP} expressing disc (g) and corresponding images of GBPAlexa555 (h) at indicated times after the acid wash (see Materials and Methods). Note that no detectable GBPAlexa555 signal is observed 40 min after the acid wash, indicating that the extracellular pool of nanobodies has been efficiently removed and that the potential extracellular leftover (below the detection limit) cannot lead to an observable recovery in intracellular compartments. i, Theoretical dynamics of GBPAlexa555 fluorescence recovery in the iFRAP experiment normalized to the prephotobleaching levels. Recovery was calculated numerically using the set of values determined experimentally for large (top) and small discs (bottom). The dashed lines indicate the estimated fraction of recovery 2,000s after photobleaching in large and small discs to compare with the experimental conditions in the iFRAP experiments (Fig. 4g). Scale bar, 10 µm (g, h).
Extended Data Fig. 6 Internalized Dpp is recycled and spreads in the tissue: Dpp^{Timer} and recycling Rab proteins.
a, Functionality of Dpp^{Timer}. Left, control disc, expressing sfGFPmKate2Dpp under the control of the GAL4/UAS expression system (Dpp^{Timer}). Centre, dpp mutant disc, the wing imaginal disc is outlined with the white dashed line. Right, dpp mutant disc expressing Dpp^{Timer}. Note that the mutant phenotype seen in the central image is rescued. b, Scatter plot of sfGFP and mKate2 pixel intensities and linear fit to obtain the calibration factor F (see Supplementary Information section 2.6.3). n = 23 beads. c, Confocal images of the Dpp^{Timer} gradient in the wing disc (sfGFP, top and mKate2, bottom). d, Relative concentration profiles of mature sfGFP and mKate2 plotted against the distance from the Dpp source (see Supplementary Information section 2.6.3), corresponding to the intensity profiles measured from the images in c. These intensity profiles represent the relative amounts of sfGFP and mature mKate2 molecules. e, Adjusted fluorescence intensity profiles for sfGFP (g^{*}(x)) and mature mKate2 (r^{*}(x)) which are proportional to the respective concentration profiles. Xaxis represents the distance from the source. Red dashed line is positioned at the anteriorposterior boundary. Note that both in the source and in the region of the target closer to the source, there are less mature mKate2 molecules, confirming that Dpp molecules are younger closer to the source. f, Plotted relative age (A(x)) of Dpp molecules as a function of position calculated from the calibrated profiles in e. Note that as molecules move away from the source they become older on average: A(x) increases to plateau at values close to 1. n, number of biologically independent samples. Shaded areas, s.e.m (e, f). g–j, Effect of pH on the Timer. g, Control of the bafilomycin treatment. Confocal images of a ROI in discs incubated with a LysoSensor^{TM} probe for 30 min before (top) and after (bottom) incubation in control Clone 8 medium (right) or bafilomycin solution (left). h, Effect of pH on sfGFP and mKate2 in the Dpp^{Timer}. Confocal images of sfGFP (left) and mKate2 (right) of Dpp^{Timer} before (top) and after (bottom) neutralization of pH to 7 following bafilomycin treatment for 30 min. i, Fluorescence signal decrease of sfGFP and mKate2 owing to acidic pH in intracellular compartments. Percentage decrease of fluorescence from pH 7 (discs after bafilomycin treatment) to the acidic environment in intracellular compartments (discs before bafilomycin treatment). Note that the decrease is very similar for both fluorophores. j, Normalized fluorescence intensity of sfGFP (blue) and mKate2 (orange) in purified Timer molecules in solutions at different pH. Data normalized to the intensity at pH 7.4. The number of biologically independent samples for this analysis: n_{pH5.86} = 8; n_{pH6.4} = 7; n_{pH7.4} = 7; n_{pH7.9} = 5. Data represented as mean values ± s.e.m. Note, that the difference between the normalized intensity of sfGFP and mKate2 at the different pH value is not significant (pvalue>0.05; twotailed two sample ttest). k, Confocal images of eGFPDpp^{LOP} in control condition (top) and after RNAi through expression of dsRNA for the recycling Rab proteins, Rab11 (middle) and Rab4 (bottom) in posterior target cells. l, Spatial fluorescence profiles of eGFPDpp^{LOP} corresponding to control (top), Rab11RNAi (middle) and Rab4RNAi (bottom) conditions in k. m, Decay length λ of eGFPDpp^{LOP} gradient versus posterior compartment length l for control (n = 157), pent^{2} discs (n = 63) and Rab4RNAi (n = 39). Dots, binned data; bars, s.e.m. Control and pent^{2} data as in Fig. 2a, Extended Data Fig. 7f. n, Average eGFPDpp^{LOP} decay length in control and Rab11RNAi conditions. Difference between the two conditions is significant as determined by a twotailed, two sample ttest with unequal variances, pvalue = 0.0034. o, Recycling rate in control and Rab4RNAi conditions, determined by the nanobody uptake assay. Number of curves for each condition is n = 4. Difference between the two conditions is significant; twotailed, two sample ttest with unequal variances, pvalue < 0.0001. Rab4RNAi expression was driven by means of the thermosensitive Gal4Gal80^{ts} system (29 °C). p–r, Scaling of eGFPDpp^{LOP}. p, Dpp gradient profiles of discs from 40 to 160 µm posterior length. Each individual profile was fitted to an exponential function with an offset (see Supplementary Information section 2.1.2) and the offset returned from the fit was subtracted. q, Normalized Dpp gradient profiles. Each profile was normalized to the amplitude C_{0} of its exponential fit in the ordinates (C(r)/C_{0}) and to the posterior length l of the corresponding wing disc in the abscissas (r=x/l). Shaded area, s.e.m. Black line, average normalized profile. r, Density plot of q: Colourcode corresponds to the fraction of the number of gradients passing through a certain r, C(r)/C_{0} bin. Scale bars, 100 µm (a) and 10 µm (c, g, h, k).
Extended Data Fig. 7 Gradient scaling by recycling: Pentagone.
a, Continuous and monotonic transition from λ ≈ 15 μm (black dashed line) to λ ≈ 27 μm (red dashed line). Left: decay length (λ) versus a parameter b that captures monotonic and continuous changes in k_{on}, k_{off} and D_{0} as shown in the right. Right: Variations in k_{on}, k_{off} and D_{0} with b as defined by the equations shown in the plot. Black and red dashed lines indicate initial (small discs) and final (large discs) values for k_{on}, k_{off} and D_{0}. b, Top: expression for the ratio of the recycling to the unbound module (λ_{r}^{2}/λ_{u}^{2}, see Fig. 1c). Bottom: Sets of parameter values (clouds of points) compatible with all the assays considered in this report in the (k_{on}, k_{off}) plane. Isolines for (λ_{r}^{2}/λ_{u}^{2} are also shown (see lookup table). The three conditions considered in this work are shown: large discs (average posterior length l = 144 µm in the dataset; left), small discs (average l = 80 µm; centre) and pent^{2} discs (right). These isolines convey the relative importance of the recycling and the unbound modules to the Dpp transport. c, PMAD scaling analysis for control and pentagone mutants. Left, Decay length λ of PMad gradients plotted as a function of posterior compartment length l. Raw and binned data (Bar, s.e.m) are shown together with a linear regression to the raw data. Right, bar plots showing the slopes ϕ of corresponding linear regressions for control (blue) and pentagone mutant experimental conditions (red). Number of biologically independent samples: n = 45 (control) and n = 25 (pent^{2}). ****pvalue < 0.00001; twotailed two sample ttest with unequal variances. Bars, confidence intervals at 95%. d, UASGFPPentagone expression driven by apGal4. In the right, higher magnification of the area boxed in the image to the left. Scale bars, 10 µm. e, GFPPentagone gradient profile in the ventral compartment. The profile is fitted to an exponential function (red) to determine the decay length shown. x, distance from the dorsoventral boundary. f, eGFPDpp^{LOP} scaling analysis for control and pentagone mutants. Left, Decay length λ of eGFPDpp gradients plotted as a function of posterior compartment length l. Raw and binned data (Bar, s.e.m) are shown together with a linear regression to the raw data. Right, bar plot showing the slopes ϕ of corresponding linear regressions from these plots. Control experimental condition (blue) compared to pentagone mutant experimental condition (red). Number of biologically independent samples: n = 157 (control) and n = 63 (pent^{2}). ****pvalue < 0.00001; twotailed two sample ttest with unequal variances. Bars, confidence intervals at 95%. g, Sets of parameter values satisfying the constraints given by all the experimental assays represented in (k_{on}, k_{off}), (k_{on}, D_{0}) and (k, k_{off}) planes in the four experimental conditions: eGFPDpp^{LOP}expressing discs of 144 µm and 80 µm average posterior length and pent^{2} mutant discs of 130 µm and 85 µm average posterior length. h, Stacked bar chart showing the relative contribution of the different modules to λ^{2} (described in Fig. 1e,f) in the four experimental conditions in e compared to the theoretical values of parameters in the extracellular diffusion (ExD) and transcytosis regimes of transport (Tr). i, Average extracellular fraction in control discs of 144 µm and 80 µm average posterior length and pent^{2} mutant discs of 130 µm and 85 µm average posterior length. Box plot represents the minimum and the maximum, median, 25^{th} and 75^{th} percentile. n, number of biologically independent samples. j, Confocal images of PentGFP from the endogenous gene in discs of different sizes. Scale bar, 10 µm. Dotted lines, contour of discs. k, PentGFP average intensity in its expression domain as a function of the squared posterior length of the wing disc; Black, binned data. Orange dots, raw data. Bars, s.e.m. Vertical boxes indicate posterior width sizes l = 144 µm (orange) and l = 80 µm (blue).
Extended Data Fig. 8 Gradient scaling by recycling: HSPGs.
a, b, Scaling analysis for control and dally mutants. Left, decay length λ of eGFPDpp (a) and PMad gradients (b) plotted as a function of posterior compartment length l. Raw and binned data (bars, s.e.m.) are shown together with a linear regression to the raw data. Right, bar plots showing the slopes ϕ of corresponding linear regressions for control experimental conditions (blue) compared to dally mutant experimental conditions (red). Number of biologically independent samples: n = 93 (control) and n = 39 (dally^{gem}) (a); n = 43 (control) and n = 36 (dally^{gem}) (b). ****pvalue < 0.00001; twotailed two sample ttest with unequal variances. Bars, confidence intervals at 95%. c, Sets of parameter values satisfying the constraints given by all the experimental assays represented in (k_{on}, k_{off}), (k_{on}, D_{0}) and (k, k_{off}) planes in the four experimental conditions: eGFPDpp discs of 144 µm and 80 µm average posterior length, pent^{2} (average length, 130 µm) mutant and dally^{gem} mutant discs (average length, 174 µm). d, Stacked bar chart showing the relative contribution of the different modules to λ^{2} (described in Fig. 1e,f) in the four experimental conditions compared to the theoretical values of parameters in the extracellular diffusion (ExD) and transcytosis regimes of transport (Tr). e, GBPAlexa555 signal intensity as a function of time in discs expressing eGFPDpp^{Gal4} in control discs (left), dally^{gem} mutant discs (middle) and control discs following treatment with PIPLC for 1h (right). Lines, fits to the phenomenological equation describing the internalized signal intensity dynamics C_{T}(t). f, Values of k_{N}, k_{r} and k_{0} estimated by the nanobody uptake assay in control discs, dally^{gem} mutant discs and PIPLC treated discs expressing eGFPDpp^{Gal4}. g, Internalized GBPAlexa555 fluorescence as a function of time in discs expressing eGFPDpp^{CRISPR} (control), discs expressing eGFPDpp^{CRISPR} and sflRNAi (sflRNAi) and control discs (no GFPDpp). Number of biologically independent samples: n = 3 for each condition. Data represented as the average curve. Shaded area, s.e.m. h, i, Confocal images of eGFPDpp^{CRISPR} (left) and internalized GBPAlexa555 (right) after 85 min of incubation with the nanobody in control discs (h) and discs expressing sflRNAi in the posterior compartment (i). Posterior compartment, to the right from the GFPDpp source boundary. j, Decay length of the eGFPDpp^{CRISPR} gradient λ as a function of the posterior compartment width l. Red line, linear regression to the raw data. bars, s.e.m. eGFPDpp^{CRISPR} was visualized by means of a nanobody uptake assay (Methods). Number of biologically independent samples n = 38. k, Slope ϕ of the linear regressions for scaling plots corresponding to eGFPDpp^{LOP} (LOP) and eGFPDpp^{CRISPR} (CRISPR). Bars, confidence intervals of the fitted slope. l, Confocal images of photoconverted GBPDendra2* in eGFPDpp^{CRISPR}expressing discs at different times after photoconversion (postconversion). Before photoconversion, discs were incubated in GBPDendra2* solution for 45 min and extracellular GBPDendra2 was removed by an acid wash, so that only internalized GBPDendra2 is remaining. PhotoconvOgradient outside of the photoconverted region. m, The values of k_{N}, k_{r} and k_{0} estimated by the nanobody uptake parameters for large discs expressing eGFPDpp^{CRISPR} versus eGFPDpp^{LOP}. Bars, confidence intervals of the fits. Number of biologically independent samples n = 10 (eGFPDpp^{CRISPR}) and n = 13 (eGFPDpp^{LOP}). Scale bar, 10 µm (h, l).
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This file contains the Supplementary Methods, Supplementary Notes, Supplementary Discussion, Supplementary Fig. 1, Supplementary Tables 1–2 and Supplementary References.
41586_2021_4346_MOESM4_ESM.avi
Supplementary Video 1 Photoconversion assay. Left, a movie combining sequentially first, a confocal image of eGFPDpp^{LOP}, then an image of photoconverted endosomal GBP–Dendra2 (Dendra2*) before (preconversion) and finally images of Dendra2* at indicated times after photoconversion (postconversion). Before conversion, following pulsechase and acid wash, only internalized GBP–Dendra2 remains. Photoconversion, to the left of the red dotted line. Note buildup of a Dendra2* gradient outside the photoconverted region. Right, average spatial distribution of GBP–Dendra2* fluorescence signal at indicated times after photoconversion. Shaded areas, s.e.m.; (n = 7 independent experiments).
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RomanovaMichaelides, M., Hadjivasiliou, Z., AguilarHidalgo, D. et al. Morphogen gradient scaling by recycling of intracellular Dpp. Nature 602, 287–293 (2022). https://doi.org/10.1038/s4158602104346w
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DOI: https://doi.org/10.1038/s4158602104346w
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