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First published online September 9, 2004
doi: 10.1242/10.1242/dev.01335

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Dpp gradient formation by dynamin-dependent endocytosis: receptor trafficking and the diffusion model

Karsten Kruse^1,*, Periklis Pantazis^2,*, Tobias Bollenbach¹, Frank Jülicher^1, and Marcos González-Gaitán^2,

¹ MPI for the Physics of Complex Systems, Nöthnitzerstrasse 38, 01187 Dresden, Germany
² MPI of Molecular Cell Biology and Genetics, Pfotenhauerstrasse 108, 01307 Dresden, Germany

View larger version (85K): [in a new window]   Fig. 1. Dpp signaling in the developing wing system. (A) Double staining of a developing wing showing the Dpp source (wing pouch, arrowhead; peripodial epithelium, asterisk) monitored by GFP (green) and cell profiles labelled with phalloidin (red). Genotype: UAS-GFP/+; dpp-gal4/+. (B) Double staining of a cryostat z-section of a developing wing at the level of the broken line in A, showing cell profiles labelled by phalloidin (red), superimposed by GFP-Dpp expression (green) in the lower panel. Genotype: dpp-gal4/UAS-GFP-Dpp. (C) Detail of GFP-Dpp localization (green) in the region of the developing wing corresponding to the yellow box in A. Phalloidin labeling (red) is superimposed to show cell profiles in the right panel. (D,E) Schematic representation of the developing wing in a xz- (D) and xy-section (E). Note the position of the Dpp source (cells filled in green to the left in E) both in the wing pouch (arrowhead) and the peripodial epithelium (red in D; asterisk). Scale bars: 50 µm. Anterior to the left.

View larger version (38K): [in a new window]   Fig. 2. Transport scheme, area of interest (AOI) and gradient formation in the DBT model. (A) Dpp transport scheme considered in this study and in Lander et al. (Lander et al., 2002). For further details, see main text. (B) Dpp transport scheme with biosynthetic route targeting the receptor directly to the plasma membrane (Alberts et al., 1994). (C) Simplified geometry of the AOI (corresponding to the broken box in Fig. 1C) as used in the calculations. (D) Total ligand concentration F (sum of free extracellular ligand concentration A, surface-bound ligand concentration B, and internal-bound ligand concentration C) as a function of the distance from the source calculated in the DBT model for different times. Unbroken curves are separated by intervals of 2 hours; broken curve corresponds to the steady state. The initial conditions were A=B=C=0, D=R0, and E=R0kp/kq for all x. Note that the total ligand concentration has been displayed in ordinates normalized to R0=wkq/kgkp which is a constant that corresponds to the steady-state surface receptor concentration in the absence of ligand.

View larger version (48K): [in a new window]   Fig. 3. Gradients in the DBT model describing a tissue with shits1 clone. Dynamics of the total ligand distribution F in the DBT model in an area of interest (AOI) of size Lx=200 µm and Ly=200 µm. The AOI contains a rectangular region, inside which the internalization rates kp and kin are reduced by a factor of 10 after t=0. This region covers the intervals 25 µmx50 µm and –25 µmy25 µm and describes the effects of a temperature shift on a shibire clone. (A) Color-coded distribution of the total ligand concentration F=A+B+C at t=5 hours. (B) Distribution of F after 48 hours, which is close to the steady state. (C-E) Total ligand concentration F along the broken lines indicated in A,B. Unbroken black lines are separated by 2 hours. The red line represents the distributions after 5 hours, the time when the observations were made in the experiments discussed in Entchev et al. (Entchev et al., 2000); the broken lines represent the steady state distributions. Note the accumulation of ligand in the clone by a factor of 10. Far away from the clone, the ligand distribution resembles the distribution in absence of a clone (compare D with Fig. 2D). The steady-state ligand concentration has a pronounced minimum behind the center of the clone (E). The inset in C displays the profile of total extracellular ligand A+B. Note that the extracellular ligand accumulates in the clone by a factor of 10 after 5 hours of endocytotic block and more than 40 times in the steady state. (F) Contrast of the shadow as a function of time. The contrast c is defined as the difference in the total ligand concentration at the points indicated by arrows in E normalized with respect to the total ligand concentration at (x=x0,y=Ly/2). Formally, c=[F(x0,Ly/2)-F(x0,0)]/F(x0,Ly/2). Note that the contrast still increases after 5 hours and that the shadow persists. Results in A-F were obtained by solving Eqns 3, 4, 5, 6, 7 with parameter values as given in Table 1 and `current boundary conditions', given by Jx=0 at x=Lx, Jx=vd/2a2 at x=0, Jy=0 at y=±Ly/2; initial conditions A=B=C=0, D=R0, as well as E=R0kp/kq.

View larger version (48K): [in a new window]   Fig. 4. Gradients in the DBTS model describing a tissue with shits1 clone. Evolution of the total ligand distribution as shown in Fig. 3, but in the DBTS model with vanishing internalization rates within a region describing the clone. (A,B) Color-coded distribution of the total ligand concentration F=A+B+C after 5 hours of endocytic block (A), and after 48 hours, corresponding to the steady state (B). (C-E) Total ligand concentration F along the broken lines indicated in A,B. Unbroken black lines are separated by 2 hours. The broken lines represent the steady state distributions, the red line the distributions after 5 hours, the time when the observations were made in the experiments discussed in Entchev et al. (Entchev et al., 2000). The inset in C shows the concentration of internal-bound ligand, which vanishes inside the clone. The profile of the ligand concentration behind the clone is shown in E. At 5 hours, a clear shadow is present which vanishes and turns into a persistent anti-shadow. (F) Contrast c of the shadow as defined in Fig. 3. The results were obtained by solving Eqns 3, 4, 5, 6, 7 in a rectangular area of interest (AOI) of size Lx=200 µm and Ly=200 µm with parameter values indicated in Table 1, `current boundary conditions', i.e., Jx=0 at x=Lx, Jx=vd/2a2 at x=0, Jy=0 at y=0 as well as at y=Ly. At t=0 initial conditions were A=B=C=0, D=R0, where and . The internalization rates are given by Eqn 9 with Rmax=20R0.

View larger version (31K): [in a new window]   Fig. 7. Concentrations of internal-bound ligand (C) in the presence of a shits1 clone calculated in the DBT and the DBTS models. (A) Replication of the one-dimensional calculations of Lander et al. (Lander et al., 2002) for the DBT model. Profiles of internal-bound ligand at 5 hours, 24 hours, and 48 hours obtained for the same parameters as in Lander et al. (Lander et al., 2002) (see Table 1) with `concentration boundary conditions' and Lx=100 µm. The endocytic block in the clone is described by a tenfold reduction of receptor internalization rates (kp, kin). In addition, at time t=0, the surface receptor concentration was suddenly increased by a factor of 10 inside the clone as described in Lander et al. (Lander et al., 2002). Note, that in order to replicate the results shown in Fig. 7 of Lander et al. (Lander et al., 2002), the receptor production rate w had also to be reduced by a factor of 10. After 5 hours the ligand concentration is reduced behind the clone as compared with the results of the same calculation in the absence of a clone (broken line). This corresponds to a shadow in the experiments. At 24 hours, the shadow is weak. This is not a steady state situation because after 48 hours, an accumulation of ligand behind the clone and depletion in the clone occur. (B) One-dimensional calculation as described in A, but with correct receptor production rate w in the clone region (not reduced by a factor of 10). A shadow builds up which increases in time and persists. (C) One-dimensional calculation as in B (i.e. corrected w), but further corrected with surface receptor concentration in the clone region which increases gradually according to the DBT model (see also Fig. 3). (D) Distribution of internal-bound ligand in a two-dimensional calculation for the DBT model with Lx=200 µm and Ly=200 µm at 5 hours, 24 hours, and 48 hours along a section through the clone in x-direction, as in Fig. 3C (unbroken line) and Fig. 3D (broken line). Note that the one-dimensional and two-dimensional calculations generate similar profiles for the geometry of area of interest (AOI) and clone size chosen (compare C and D). Note also that in both cases there is a shadow that persists in the steady state. (E) Ligand distributions as described in D, but obtained for the DBTS model for saturating surface receptors and zero internalization rates. A shadow is present at 5 hours and has disappeared at 24 hours. There is no internal-bound ligand inside the clone. In A-E, the clone extends from x=25 µm to x=50 µm. (F) Total surface receptor concentration, B+D, in the center of the clone. The dotted line corresponds to the calculation shown in A, the broken line to B, and the unbroken line to the calculation shown in D (a similar profile corresponds to C). (G) Total surface receptor concentration, B+D, in the center of the clone for the calculation shown in E.

View larger version (128K): [in a new window]   Fig. 5. Extracellular GFP-Dpp and Thickveins localization in shits1 clones. (A,C) Double labelings showing GFP-Dpp distribution (green), total (A) or extracellular (C) GFP immunostaining (red) and overlays. (B,D) Fluorescence intensity profiles of GFP-Dpp (green) and total (B) or extracellular (D) GFP immunostaining (red) in representative discs. Genotype in A-D: dpp-gal4/UAS-GFP-Dpp. (E) Double labeling showing shits1 clones after 5 hours at the restrictive temperature (see Materials and methods) marked by the absence of Nmyc (red), and Tkv immunostaining (green). Genotype shits1 FRT18A/HS-NM8A FRT18A; HS-Flp/+. Note that the levels of Tkv outlining the cells are not significantly changed within the mutant mosaics. (F,G) Double labeling showing shits1 clones after 5 hours at the restrictive temperature marked by the absence of DsRed (red) and immunostaining of surface exposed Tkv using the Tkv luminal antibody and the `extracellular immunostaining protocol' (green; see Materials and methods). Genotype: shits1 FRT18A/tub-DsRed FRT18A; HS-Flp/+. Note that the levels of surface exposed Tkv are not increased within the shits1 mutant clones. White line: clone outline. Scale bars: 10 µm in A-E; 50 µm in F,G.

View larger version (110K): [in a new window]   Fig. 6. `Shibire rescue assay' and the DBTS model. (A-C) Ligand and receptor distributions corresponding to the situation in the `shibire rescue' experiment calculated in the DBTS model containing a region –10 µmx0 µm describing secreting cells. Lines are separated by intervals of 1 hour. At t=0, we assume that endocytosis is blocked in the tissue for x0 µm. (A) Total ligand concentration F=A+B+C. (B) Total extracellular ligand concentration A+B, (C) total surface receptor concentration B+D. Broken lines indicate the concentrations at t=0 given by the steady-state value obtained for parameter values describing a WT tissue. The endocytosis block is modeled by setting the receptor internalization rates to zero for x0 µm. The red lines show the concentration after 6 hours, the time at which the experimental observations are made. The calculations are performed in one dimension with an AOI of size Lx=200 µm, with `current boundary conditions' and parameter values as specified in Table 1. (D-I) Extracellular GFP-Dpp and Thickveins localization in the `shibire rescue' experiment. (D,E) Double labeling showing GFP-Dpp (green) and immunostaining of extracellular GFP-Dpp (red) from a shits1; UAS-Dynamin+/+; dpp-gal4/UAS-GFP-Dpp larva (D) or from a heterozygous shits1/+ sibling (E) incubated at 34°C for 6 hours. Note that the range of extracellular GFP-Dpp in the hemizygous wing disc is reduced after 6 hours of block at the restrictive temperature. (F) Intensity profiles of extracellular GFP immunostainings in representative discs. Red trace, GFP in a heterozygous sibling. Blue trace, GFP in a hemizygous sibling. Green box, secreting cells. Extracellular GFP-Dpp drops significantly in the receiving tissue when endocytosis is abolished. (G,H) Double labeling showing GFP-Dpp (green) and immunostaining of Tkv (red) from a shits1; UAS-Dynamin+/+; dpp-gal4/UAS-GFP-Dpp larva (G), or from a heterozygous shits1/+ sibling (H) incubated at 34°C for 6 hours. We also noted a downregulation of Tkv levels of unknown significance abutting the A/P boundary. (I) Intensity profiles of Tkv immunostaining in representative discs. Red trace, Tkv in a heterozygous shits1/+ sibling. Blue trace, Tkv in a hemizygous shits1 sibling. Tkv-levels do not change in the receiving tissue when endocytosis is abolished for 6 hours. (J,K) Double labeling showing GFP-Dpp (green) and immunostaining of cell surface exposed Tkv using the Tkv luminal antibody and the `extracellular immunostaining protocol' (red) from a shits1; UAS-Dynamin+/+;dpp-gal4/UAS-GFP-Dpp larva (J), or from a heterozygous shits1/+ sibling (K) incubated at 34°C for 6 hours. (L) Intensity profiles of cell surface exposed Tkv immunostaining in representative discs. Red trace, Tkv in a heterozygous shits1/+ sibling. Blue trace, Tkv in a hemizygous shits1 sibling. Surface Tkv levels do not significantly change in the receiving tissue when endocytosis is abolished for 6 hours. In D,E,G,H,J and K broken lines delimit the Dynamin+ rescued source. Scale bars: 10 µm.