Extended Data Fig. 4: Parameterization assay controls II: FRAP, extracellular fraction determination and parameter estimation by ABC.
From: Morphogen gradient scaling by recycling of intracellular Dpp
a, Left, confocal image of the eGFP-DppLOP gradient in a FRAP experiment (source and posterior compartment). Red box, region to be photobleached. Right, eGFP-DppLOP fluorescent signal in the red box region before photobleaching (−1 min) and at different times (as indicated below) after photo-bleaching. 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 pent2 mutant disc). Data represented as mean values. Bars, s.e.m. Lines, calculated recovery using the five-pool theoretical framework for a set of parameter values. The coefficient of determination R2 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 equation3. Dependence of the goodness of the fit (R2) to this single dynamic equation (c) and the effective diffusivity (Deff) 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 pent2 discs (right). Bars, confidence intervals (d). In d data are represented as Deff estimated by fit for varying number of independent recovery curves, n. Bars, confidence intervals of fit. e, Effective diffusivity (Deff, left) and effective degradation rate (keff, 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 equation3 to determine Deff and keff. Note, that as discs grow, Deff does not change significantly, whereas keff decreases significantly, as previously reported23. Data is represented as Deff and keff estimated by fit. Bars, confidence intervals of fit. n, number of biologically independent samples. One-tailed two sample t-test with unequal variances; p-values: 0.1765 (Deff, left) and 0.0038 (keff, right). f, Simulated intensity profile of eGFP-DppLOP 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 eGFP-DppLOP gradient (left; total pool), and the extracellular eGFP-DppLOP pools monitored by means of an extracellular immunostaining (see Supplementary Information section 2.3) by using a GBP-Alexa555 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 GBP-Alexa555 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 GBP-Alexa555 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 GBP-Alexa555 and GFP concentrations (determined by BCA) in the solutions. The relative concentration of GFP and GBP-Alexa555 can be determined from the relative concentration at which the minimum value (rmin) of GFP fluorescence has been reached. Note that rmin ≃ 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 (kon, koff) plane. Light orange area represents the full space of 3 × 107 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 steady-state decay length, the long-term FRAP assay, the nanobody internalization and the FRAP assay. Calculated FRAP recovery curves using these sets of values fit the experimental FRAP data with R2>0.92. Note that the solutions are separated into two clusters (clouds): the upper cloud, with higher kon, koff, 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 (koff, kon), (koff, k), (D0, kon) and (ko, kon) 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).
