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
Authors for correspondence (e-mail:
gonzalez{at}mpi-cbg.de;
julicher{at}mpipks-dresden.mpg.de)
Accepted 28 June 2004
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SUMMARY |
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Key words: Drosophila, Morphogens, TGFß
![]() |
Introduction |
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Although the concept of morphogenetic signaling, first formulated by Turing
(Turing, 1952) and modified by
Wolpert (Wolpert, 1969
), has
pervaded the field of developmental biology, the cell biological basis of the
spreading phenomenon itself for each particular morphogen molecule is still a
matter of controversy (reviewed by
González-Gaitán,
2003
; Vincent and Dubois,
2002
). Two scenarios for the dominant mechanisms of transport have
been mainly discussed: extracellular diffusion and planar transcytosis, i.e.
endocytosis and resecretion of the ligand that is thereby transported through
the cells (reviewed by
González-Gaitán,
2003
; Vincent and Dubois,
2002
).
In the case of the Drosophila TGF-beta-superfamily homolog Dpp,
both diffusion and planar transcytosis have been proposed as transport
mechanisms (Entchev et al.,
2000; Lander et al.,
2002
) (reviewed by
González-Gaitán,
2003
). Dpp is expressed within a narrow stripe of cells in the
center of the developing wing epithelium
(Basler and Struhl, 1994
), from
where it is secreted and forms a long-range gradient of concentration across
40 cell diameters (Entchev et al.,
2000
; Teleman and Cohen,
2000
). In experiments in which Dpp is pulsed from the source, the
graded profile of Dpp concentration expands rapidly and reaches its steady
state range of 40 cell diameters in less than 8 hours
(Entchev et al., 2000
;
Teleman and Cohen, 2000
). In
addition, Dpp spreads equally in all directions.
The proposal that intracellular Dpp trafficking is implicated in its
long-range dispersal stemmed from mosaic experiments in which endocytosis was
impaired in mutant patches of cells: the `shibire rescue assay', the `shibire
shadow assay' and the `Rab mutant assays'
(Entchev et al., 2000). In the
`shibire rescue assay', the source is wild-type (WT), whereas the target
tissue is endocytosis-defective because of a Dynamin thermosensitive mutation
(shibirets1, shits1)
(Chen et al., 1991
). In this
condition, Dpp is not internalized in the target cells and its range is
restricted to the cells adjacent to the source. In the `shibire shadow assay',
Dpp spreading from the source is confronted with an endocytosis-defective
mutant patch of cell. In this situation, Dpp is unable to spread across the
clone and forms a shadow distal to the clone. The shadow is transient and is
finally filled by Dpp moving rapidly and in all directions from the sides of
the clone. Finally, in the `Rab mutant assay', mutants for key Rab GTPases
involved in the endocytosis/early endosomal dynamics (Rab5) or degradation
(Rab7) are expressed in the receiving cells. When endocytosis is impaired or
degradation is enhanced, the signaling range is reduced, whereas, conversely,
an enhanced endocytosis/endosomal dynamics leads to an expansion of the
signaling range. These data support the idea that Dpp dispersal is mediated by
endocytosis and resecretion of the ligand in the receiving cells. In the
absence of endocytosis, extracellular diffusion contributes only to spreading
over a short-range (across 3-5 cells)
(Entchev et al., 2000
).
However, the Dpp re-secretion event itself has not yet been directly
monitored.
In general, ligand transport depends on complex non-linear kinetics, such
as the kinetics of receptor binding/release and the kinetics of trafficking of
ligands and receptors. Therefore, a quantitative analysis based on
mathematical models is essential in order to establish that the observed
ligand dynamics indeed emerge from a particular mechanism. Ligand dispersal
has been early described theoretically using reaction-diffusion equations
(Gierer, 1981;
Gierer and Meinhardt, 1972
;
Koch and Meinhardt, 1994
;
Turing, 1952
). Such
theoretical approaches are useful to study robustness and precision in
morphogen gradient formation (Eldar et al.,
2002
; Eldar et al.,
2003
; Houchmandzadeh et al.,
2002
) and have suggested that simple diffusion may not suffice to
generate graded profiles of receptor occupation
(Kerszberg and Wolpert, 1998
).
Furthermore, ligand trafficking in cells has been studied theoretically and a
possible role of transcytosis to enhance transport efficiency has been
proposed (Chu et al., 1996
;
Lauffenburger and Linderman,
1993
).
A recent theoretical analysis of Dpp spreading indicates, though, that
transcytosis does not play an important part in this process
(Lander et al., 2002). The
properties of transport based on extracellular diffusion were studied using a
model that takes into account diffusion and receptor binding. It was suggested
that this `diffusion, binding and trafficking' (DBT) model can generate ligand
profiles which are consistent with WT gradients and the results observed in
the `shibire shadow assay' (Lander et al.,
2002
). A block of endocytosis could induce a higher level of
surface receptors and thereby titrate out the pool of spreading free ligand,
obstructing the ligand transport (Lecuit
and Cohen, 1998
). Lander et al. argued that this scenario
generates a transient shadow. They solved reaction-diffusion equations in a
one-dimensional geometry, suggesting that this description suffices to capture
key features of these experiments.
Here, we perform a theoretical analysis of the DBT model in one and two dimensions. We discuss the role of the geometry, the appropriate boundary conditions, and the initial conditions in the `shibire shadow assay' and the `shibire rescue assay'. We then determine experimentally the levels of receptors and extracellular Dpp to compare them with the ligand and receptor profiles obtained in the DBT model. We show that although the DBT model cannot account for the observed transient shadows, a modified version of the model, introducing surface receptor saturation, is consistent with such shadows. However, the receptor and ligand profiles under this modified DBT model are inconsistent with the observed levels in the `shibire shadow' and `shibire rescue' experiments. We therefore conclude that current models in which transport occurs exclusively in the form of extracellular diffusion cannot explain the experimental data, suggesting that endocytosis plays an active role in the ligand transport beyond the regulation of receptors at the surface.
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Materials and methods |
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Mutant strains
shits1 and tkv8 are described in
Flybase
(http://flybase.bio.indiana.edu).
tkv8 is a Tkv receptor truncated at amino acid 144 before
the transmembrane domain that presumably represents a null mutation of
tkv (Nellen et al.,
1994). UAS-Dynamin, UAS-Tkv and UAS-GFP-Dpp were
previously described (Entchev et al.,
2000
; Nellen et al.,
1996
). UAS-GFP was graciously provided by Barry Dickson
(Institute of Molecular Pathology, Vienna, Austria). The tub-DsRed
construct was inserted into a P-element plasmid containing the promoter of the
tubulin
1 gene and flanked at its 3' end by the 3' UTR of
the tubulin
1 gene (Basler and
Struhl, 1994
). Tub-DsRed was recombined onto FRT18
chromosome to allow the generation of somatic clones by Flp-mediated mitotic
recombination (Xu and Harrison,
1994
).
Antibodies and immunostainings
Rabbit anti-Tkv antibody was generated against two peptides corresponding
to parts of the intracellular kinase domain (H2N-SQQLDPKQFEEFKRAC-CONH2 and
H2N-GFRPPIPSRWQEDDVC-CONH2). Rabbit luminal anti-Tkv antibody was generated
against two peptides corresponding to the luminal side of the Tkv peptide
sequence outside the ligand binding cleft (H2N-YEEERTYGCMPPEDNG-CONH2 and
H2N-KEDFCNRDLYPTYTP-CONH2). The immune sera were affinity chromatography
purified using the corresponding Tkv peptides coupled to CNBr-activated
Sepharose 4B (Amersham Biosciences). The specificity of the antibodies was
tested by preincubating the purified antibody with 100 µg/ml Tkv peptide
(or 500 µg/ml when performing the `extracellular immunostaining protocol
with luminal anti-Tkv antibody') for 30 minutes at room temperature and
performing subsequently an antibody staining on Tkv-overexpressing discs. No
fluorescent signal was detected under these conditions, whereas preincubation
with a control peptide did not affect the staining. Immunostainings were
performed as previously described (Entchev
et al., 2000) using Mouse anti-Myc, 1:25 dilution; Rabbit anti-Tkv
(intracellular), 1:125; Goat anti-GFP, 1:100. Extracellular GFP-Dpp and cell
surface-exposed Tkv were detected by incubating prior to fixation
(Strigini and Cohen, 2000
)
with Goat anti-GFP antibody, 1:10 dilution, and Rabbit anti-Tkv (raised
against the luminal domain of Tkv), 1:10 dilution, respectively. Dimmer
GFP-Dpp signal was found upon extracellular immunostaining compared with the
normal staining because of the different washing procedures. To estimate
GFP-Dpp range in number of cells, a fluorescent phalloidin (Molecular Probes)
counterstaining was performed to monitor the cell profiles. Cryostat
z-sections at Cryo-Star HM 560 (Microm) were performed with PFA-fixed
developing wing discs incubated for at least 12 hours at 4°C in 30%
sucrose solution in PBS and mounted with Tissue-Tek (Sakura). Images were
acquired in a Zeiss LSM510 confocal microscope and processed using Adobe
Photoshop 7.0 (Adobe Systems). Quantifications were done with Image J
(NIH).
Mosaics
tkv8 mutant Minute+/FRT clones
(Xu and Harrison, 1994) were
generated by heat shock (30 minutes, 36°C) in 3-day-old larvae
(HS-Flp/+; M(2)z PMyc FRT40A/tkv8 FRT40A) and raised at
25°C to mid-third-instar larvae. To induce PMyc transcription larvae were
heat-shocked at 38°C for 1 hour followed by at least 1 hour at 25°C to
allow the translation of the PMyc transcript prior to fixation.
shits1 FRT mutant clones were generated in larvae of the
genotype shits1 FRT18A/HS-NM8A FRT18A; HS-Flp/+ and
shits1 FRT18A/tub-DsRed FRT18A; HS-Flp/+, respectively.
Embryos were collected during one day at 18°C, larvae were raised for one
day at 18°C and heat-shocked (90 minutes, 38.3°C). Larvae were
subsequently kept at 25°C until third-instar larval stage. Afterwards,
endocytosis was blocked either for 3 hours at 34°C followed by 1 hour at
38.3°C to induce both NMyc transcription and shibire block and 1 hour at
34°C to allow the translation of the NMyc transcript, or for 5 hours at
34°C in the case of larvae of the genotype shits1
FRT18A/tub-DsRed FRT18A; HS-Flp/+. Dissection of wing discs was performed
at 34°C.
Blockage of endocytosis at receiving cells
shits1; UAS-Dynamin+/+; dpp-gal4/UAS-GFP-Dpp
larvae were kept at the shits1-permissive temperature
(25°C or 18°C) to allow normal wing development until third-instar
larval stage, when endocytosis was blocked for 6 hours at 34°C. Wing discs
were dissected and fixed.
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Results |
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![]() | (1) |
![]() | (2) |
![]() | (3) |
![]() | (4) |
![]() | (5) |
![]() | (6) |
![]() | (7) |
![]() |
|
|
We are interested in the formation of a Dpp gradient in a particular area of the primordium. Fig. 1C and Fig. 2C define this AOI. The AOI corresponds to a rectangular piece of tissue in the primordial cell layer located in the posterior compartment and adjacent to the Dpp source (Fig. 1C, Fig. 2C). It extends Lx=200 µm (50 cells) in the x-direction and Ly=200 µm (50 cells) in the y-direction (Fig. 2C). In principle, we need to take into account the complete geometry of the wing disc in order to have a full mathematical description of the ligand kinetics. However, the ligand kinetics within the AOI depends only weakly on the kinetics outside, provided the size of the AOI is sufficiently large (see below).
Boundary conditions
Because we describe an AOI of finite extension, the currents of ligand
entering and leaving the AOI at its boundaries have to be specified. Along the
boundary adjacent to the secreting cells at x=0 (`source boundary';
Fig. 2C), cells expressing Dpp
inject the morphogen into the AOI. A cell of width a (approximately 4
µm) secretes Dpp at a constant rate, which is denoted by and measured
in Moles/s (Fig. 2A,C). A
single cell contributes to a Dpp current into the AOI of magnitude
/2a along the x-direction. Here, the factor two takes
into account that Dpp leaves the source in two directions (towards anterior
and posterior) and only half of the secreted ligand reaches the posterior
compartment. The total current entering the AOI is increased by a factor
d/a, which is the number of contributing cells. Here,
d
20 µm denotes the width of the stripe of secreting cells
(Fig. 2C). For simplicity, we
assume that the Dpp source is homogeneous along the y-direction. The
source boundary condition at x=0 is thus given by:
![]() | (8) |
Let us consider the boundary at x=Lx on the
opposite side of the AOI with respect to the source (`distal boundary';
Fig. 2C). An outflux of ligand
across this boundary is present which becomes small if the ligand
concentration nearby is small. We expect the current across the boundary
sufficiently far from the source to be small enough to be neglected and impose
the current to be zero at the boundary. We choose the width
Lx of the AOI, such that this choice of boundary condition
does not affect the ligand distribution in the region where the gradient
develops. Indeed, one can show that for Lx200 µm
the choice of the `distal boundary' condition becomes irrelevant (see Fig. S3
in the supplementary material).
At the remaining boundary lines y=Ly/2 and y=+Ly/2 of the AOI (`side boundaries'; Fig. 2C), we also impose `zero current' conditions across the boundary line, Jy=0. In the simplest case, in which the whole system is homogeneous in the y-direction, this condition is satisfied automatically. An example for the formation of a graded ligand profile using these boundary conditions (`current boundary' conditions) is displayed in Fig. 2D. A more interesting case arises if a patch of genetically modified cells (a clone) is present in the system. Then, ligand and receptor concentrations will vary along the y-coordinate and a current can cross the boundaries at y=Ly/2 and y=+Ly/2. However, if the boundaries are located sufficiently far away from the clone, the ligand concentration in the vicinity of the clone is not affected by our choice of boundary conditions. For a clone of size 50 µm, we observed that the choice Ly=200 µm results in concentration profiles that are independent of the specific boundary conditions imposed (see supplementary material).
Dpp depletion behind shits1 clones
The role of endocytosis during Dpp gradient formation has been studied by
inducing a patch of thermosensitive Dynamin mutant cells, a
shits1 clone, into a wing disc
(Entchev et al., 2000). In this
experiment, GFP-Dpp expression in the source was triggered using the
thermosensitivity of the driver system. The experiment is performed under the
following initial conditions: (1) Non-tagged endogenous Dpp is also expressed
in the disc and is presumably in a steady-state distribution, because
normal-looking adults emerge when applying these temperature conditions in WT
animals; and (2) the thermosensitive Dynamin mutant cells can perform
endocytosis at the permissive temperature (25°C) at t=0. The
experiment starts by elevating the temperature (34°C), which causes an
immediate block of endocytosis in the clone, and an immediate onset of GFP-Dpp
production in the source.
Under these conditions, GFP-Dpp is entering the target tissue. When
confronted with the endocytosis-defective Dynamin mutant clone, a `shadow', a
region with reduced GFP-Dpp concentration distal to the clone, is generated.
This shadow can only be observed for a limited time: after several hours, the
shadow region is indistinguishable from the adjacent regions. This result
provides evidence that endocytosis is essential for the long-range movement of
Dpp. Based on this and the `shibire rescue assay' (see below), a working model
was proposed in which free diffusion of Dpp only accounts for short-range
spreading of Dpp, and long-range movement of Dpp is mediated by repeated
rounds of internalization and resecretion through the receiving cells
(Entchev et al., 2000).
We now address the question of whether the DBT model can account for the formation of a transient shadow behind the clone. For this purpose, we solve the DBT dynamic Eqns 3, 4, 5, 6, 7 using the `current boundary conditions' discussed above. We perform a two-dimensional calculation representing the clone by a rectangular region. In this region the internalization rates for the free- and the bound-receptor kin and kp are abruptly reduced at t=0 in order to model an impaired endocytosis.
A rapid reduction of the receptor internalization rates is consistent with
the observation that endocytosis is blocked within seconds in the
thermosensitive dynamin mutant (Entchev et
al., 2000; Ramaswami et al.,
1994
). In the DBT model, completely blocking endocytosis would
correspond to setting the internalization rates kin and
kp to zero. However, this leads to an unrealistic
unlimited increase of the cell surface receptor concentration. There are two
obvious ways to limit the surface receptor concentration: introducing surface
receptor saturation by defining the externalization rates of the receptor as a
function of surface receptor concentration, and reducing internalization rates
to a non-zero value. The effects of surface receptor saturation are discussed
in the next section. In this section, the internalization rates are reduced by
a factor of 10.
In our calculations, the initial receptor concentrations in the whole AOI are set to the WT steady-state values in the absence of ligands. The resulting concentration profiles in the presence of a clone are displayed in Fig. 3A-E. Behind the clone, the concentration exhibits a clear minimum along the y-axis in the ligand concentration (Fig. 3A,E). This minimum reflects a depletion or `shadow' that is reminiscent of the Dpp depletion observed by Entchev et al. However, in contrast to the experiments, in which the shadow disappeared with time, the DBT model does not generate transient shadows, but instead shadows become more pronounced with time and persist in the steady state (Fig. 3E). The contrast of the shadow can be quantified by comparing the total ligand concentrations at the points indicated by the arrows in Fig. 3E. As the Dpp gradient is built up, the contrast increases monotonously and attains a steady-state value with maximal contrast (Fig. 3F).
|
A DBT model with saturating cell surface receptor concentration (DBTS) can generate transient shadows behind a shibire clone
The DBT model becomes biologically meaningless if internalization rates
become zero, because in this case the level of surface receptors tends to
infinity. It is therefore not possible to describe the extreme case in which
the endocytotic block is complete. However, at the restrictive temperature the
internalization in shibire mutants is negligible
(Entchev et al., 2000;
Verstreken et al., 2002
).
Therefore, we modify the DBT model to include the saturation of surface
receptor levels. This allows us to freely vary the internalization rates and
even set them to zero.
Surface receptor levels saturate at some maximal density
Rmax. In the DBTS model (Diffusion, receptor binding and
trafficking with surface receptor saturation), we assume that the rates of
delivery to the plasma membrane (`externalization') of the free receptor
kq and that of the bound receptor kout
are a function of the total surface receptor level B+D as
follows:
![]() | (9) |
Here, the parameters and
are equal to the originally
introduced externalization rates. For small surface receptor concentrations
B+D, the DBTS model corresponds to the original DBT model.
As B+D approaches Rmax, the
externalization rates kq and kout tend
to zero. In biological terms, this would correspond to a situation in which
the externalization rates of the receptor depend on a limiting factor(s) that
can thereby be saturated, such as the trafficking machinery, cargo receptors,
etc.
The profiles of total (Fig. 4A-E) and internal bound (inset in Fig. 4C; see also Fig. 7E) Dpp have been obtained by a calculation of the DBTS model in two dimensions and in the presence of a clone. Inside the clone, the internalization rates kp and kin have been set to zero at t=0. The profile in the y-direction behind the clone displays a pronounced transient shadow similar to the experimental observation (Fig. 4A,C-E), followed by a weak persistent accumulation of ligand behind the clone (`anti-shadow') after long time periods (Fig. 4B-E). The corresponding contrast of this shadow attains a maximum after a few hours (Fig. 4F). The emergence of a shadow is a consequence of a rapid 20-fold increase of the surface receptor concentration inside the clone (Fig. 7G). In order to obtain such a rapid increase in the surface receptor concentration, the externalization and internalization rates had to be increased (by at least a factor of 10) compared with the values used in the DBT model (Table 1).
|
|
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In summary, the DBTS model can generate Dpp profiles outside of the clone that qualitatively resemble the ones observed, although anti-shadows have not been observed experimentally. Note that the DBT and the DBTS model require a drastically increased surface receptor concentration within the clone in order to create significant shadows. This generates a large accumulation of surface-bound ligand inside the clone in both models.
The DBT and DBTS models are inconsistent with the observed ligand and receptor concentrations in shibire clones
The DBT model can generate morphogen gradients similar to those seen
experimentally in the absence of a clone
(Fig. 2D). In particular, the
steady-state profiles of total Dpp and extracellular Dpp, monitored with a
specific extracellular GFP-Dpp immunostaining
(Strigini and Cohen, 1999)
(Fig. 5), resemble the profiles
obtained by the DBT model for total (Fig.
2D) and extracellular Dpp (not shown). In addition, the time
needed to form the gradient upon a pulse of Dpp from the source
(Fig. 2D) is consistent with
experimental observations in which the gradient expands until it reaches a
steady state 6 to 8 hours after the initiation of the pulse
(Entchev et al., 2000
).
|
We first consider the cell surface receptor concentration. The essential
prerequisite for forming a shadow in the DBTS model is a rapid accumulation by
a factor of 10-20 of surface receptors in the clone
(Fig. 7G). In order to compare
this with the actual surface receptor levels in the clone, we raised an
antibody that specifically recognizes the Dpp receptor, Tkv. Confirming the
results published in Teleman and Cohen
(Teleman and Cohen, 2000), we
find that the receptor accumulates predominantly at the cell surface, although
some intracellular vesicular structures can also be observed (see Fig. S5A in
the supplementary material). The level of the Tkv protein follows the
accumulation of the Tkv transcript, which is distributed in a graded fashion
complementary to the Dpp gradient (Lecuit
and Cohen, 1998
) (Fig. S5A). The antibody specifically recognizes
Tkv because it: (1) detects a corresponding band of 63 kDa in western blot
experiments from developing larvae (not shown); (2) detects overexpression
levels of Tkv, induced by the Gal4 system using a ptc-gal4 driver
(Fig. S5B); (3) is titrated out by incubating it, prior to immunostaining,
with the peptide used to raise the antibody (Fig. S5C); and (4) does not stain
cells lacking Tkv in mutant mosaics (Fig. S5D). In addition, quantitative
RT-PCR experiments show that our antibody-staining conditions can robustly
detect overexpression levels above 5-fold (Fig. S5B and not shown).
We then addressed whether the levels of surface Tkv are altered in shibire
mutant clones when endocytosis is blocked.
Fig. 5E shows that in the
shibire mutant cells after 5 hours at the restrictive temperature (the
experimental conditions that generated the Dpp shadows in the shibire clones),
the levels of receptors associated to the cell membranes are not changed. This
result indicates that even though endocytosis is blocked during 5 hours,
surface receptor levels do not change tenfold or more. To confirm that the Tkv
pool associated to the cell profiles correspond to Tkv on the cell surface, we
generated an antibody directed against the luminal domain of Tkv (see
Materials and methods) and performed the `extracellular immunostaining'
protocol (Strigini and Cohen,
1999). We determined the specificity of this antibody following
the same criteria discussed above (Fig. S5E-G). As with the other Tkv
antibody, our antibody staining in this condition can robustly detect
overexpression levels above 5-fold (Fig. S5), as monitored by RT-PCR (not
shown). Figs 5F,G show that the
levels of surface Tkv are not affected upon 5 hours of endocytic block in the
shibire mutant clones. The observed shadow can therefore not result from a
mechanism based on a high surface Tkv receptor concentration as in the DBT and
DBTS models.
According to the DBT model, the levels of internalized Dpp are
significantly increased inside the clone after long time periods
(Fig. 7C,D). This may seem
surprising when internalization is blocked. The effect is because decreased
internalization by a factor of 10 leads to an accumulation of the surface
receptors, which in turn increases the levels of receptor-mediated endocytosis
of Dpp. Such an effect was not observed inside the shibire clone in which the
levels of intracellular Dpp were reduced after 5 hours (M.G.-G., unpublished)
(Entchev et al., 2000). A
reduced internal Dpp concentration is achieved in the DBTS model if the
internalization rates inside the clone are set to zero
(Fig. 7E, Fig. 4C, inset). Furthermore,
in the DBT model, the total concentration of ligand inside the clone is
significantly higher as compared with outside the clone
(Fig. 7B).
Finally, note that both for the DBT
(Fig. 3C, inset) and the DBTS
model (not shown), the extracellular level of ligand is significantly
increased in the clone. Such an extracellular accumulation of Dpp was not
observed (Entchev et al.,
2000).
Both DBT and DBTS models are inconsistent with the observed ligand and receptor concentrations in the `shibire rescue assay'
The `shibire rescue assay' allows us to monitor how blocking endocytosis in
the receiving cells has an effect on the formation of the Dpp gradient and on
the levels of intracellular and extracellular ligand and receptor
(Entchev et al., 2000). In
these experiments, the receiving cells cannot perform endocytosis at the
restrictive temperature in a shibire mutant animal, whereas the
secreting cells are rescued with a Dynamin+ transgene and
can thereby perform endocytosis normally (see Materials and methods). At the
permissive temperature, a GFP-Dpp gradient forms in the target tissue. After a
temperature shift to the restrictive temperature, endocytosis is blocked in
the receiving cells. Upon 6 hours of endocytic block, internalized Dpp has
disappeared and no gradient can be observed
(Entchev et al., 2000
).
We use the DBTS model to calculate ligand profiles under conditions that
correspond to this shibire rescue experiment. We modify the AOI and include a
region with 10 µm<x<0 representing half of the stripe of
producing cells (Fig. 2C). This
region is described by the DBTS model with the same parameters as before, but
in addition each cell in this region also secretes ligand with rate .
Because of the symmetry of the source, we now impose zero ligand current as a
boundary condition at x=10 µm (see supplementary material).
In WT, endocytosis is active and the ligand-concentration profiles
(Fig. 6A, broken line) closely
resemble those obtained without explicitly describing the source
(Fig. 2D).
|
After 6 hours of endocytic block in the `shibire rescue' discs (modeled by
setting the internalization rates in the target tissue to zero), the
calculated total (Fig. 6A, red
line) and extracellular ligand (Fig.
6B, red line) distributions in the DBTS model changes by a factor
of up to four (total) and up to ten (extracellular) in the receiving tissue
and generate a long-range gradient of high levels of Dpp. In contrast, when we
monitor total and extracellular Dpp after 6 hours of the endocytotic block at
the restrictive temperature in the experiments, the Dpp concentration
decreases and the range of the extracellular Dpp gradient is reduced
(Fig. 6D-F)
(Entchev et al., 2000).
Notably, whereas the DBTS model exhibits a discontinuous behavior of the
external ligand concentration between the WT source and the receiving tissue
with blocked endocytosis (Fig.
6B), no such discontinuity is observed in the experiment
(Fig. 6D-F).
We also investigated the surface receptor levels in the `shibire rescue
assay'. The DBTS model generates a discontinuity of the levels of surface
receptors by a factor of 20 in the receiving cells when compared with the
source after 6 hours of the endocytic block
(Fig. 6C, red line). To monitor
the surface receptor levels, we performed Tkv immunostainings in the `shibire
rescue' discs after endocytic block. No significant increase in the receptor
levels between the WT source and the receiving cells could be found
(Fig. 6G-I). Furthermore, the
levels of surface Tkv were not increased in the mutant cells as determined by
`extracellular immunostaining' (Strigini
and Cohen, 1999) using the antibody directed against the Tkv
luminal domain (Fig. 6J-L).
The `shibire rescue assay' was compared with results of the DBTS model. The distributions of both the extracellular ligand and the surface receptor densities remain qualitatively the same in the DBT model as in the DBTS model (not shown). Our comparison of experiment and theory therefore leads to the conclusion that high surface receptor levels cannot be the origin of the shadows in the `shibire shadow assay'.
![]() |
Discussion |
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![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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Three points lead to this conclusion. First, a DBT model of the `shibire
shadow assay' generates permanent shadows (Figs
3,
7), whereas the experimental
shadows are transient (Entchev et al.,
2000). Second, the DBTS model can generate transient shadows, but
only if the surface receptor levels in the clone increase dramatically
(Fig. 4). This leads to a
strong increase in the levels of extracellular ligand in the clone
(Fig. 4C). Using receptor
antibodies in the `shibire shadow assay', we did not observe these higher
levels of surface receptors in the clone
(Fig. 5E-G). Similarly, the
levels of extracellular ligand were not increased in the clone
(Entchev et al., 2000
). Third,
in the DBTS model for the `shibire rescue assay', the levels of both the
extracellular Dpp and the surface receptors are dramatically increased in the
endocytosis-defective target cells as compared with the WT source
(Fig. 6B,C). Such an increase
is not seen experimentally (Fig.
6D,G). Instead, extracellular Dpp enters the receiving tissue over
a distance of only 4-5 cells in steady-state
(Fig. 6D,F). This is in
contrast to both DBT and DBTS models of the `shibire rescue assay' in which
ligand can enter the tissue over large distances. Therefore, in addition to
downregulating surface receptors, endocytosis is likely to play additional
roles in the transport of ligands during gradient formation.
These three caveats of the DBT/DBTS models are actually not caused by the
choice of a particular set of parameters. The parameter values used in our
calculations (Table 1) were
chosen in such a way, that the typical distance over which the ligand gradient
extends as well as the characteristic time to reach steady state are
consistent with the experimentally observed profiles. Furthermore, if
possible, parameters were chosen similar to values measured for the EGF
receptor in a cell culture system (Table
1). In the case of the DBT model they are the same parameters used
in Lander et al. (Lander et al.,
2002) when they studied the diffusion model. Note that our results
showing that a high surface receptor concentration inside the clone is
required for shadows to appear is independent of any choice of parameters.
Furthermore, convincing shadows appear in the DBT and DBTS models only for
values of koff, which are small compared with those
typically measured in related systems
(Table 1). It will be necessary
to estimate the actual parameter values for Dpp during wing morphogenesis in
order to ultimately understand its mechanism of spreading (see below).
Models for morphogen transport: importance of dimensions, AOI size and boundary conditions
The geometry and boundary conditions discussed here differ from those
introduced in Lander et al. (Lander et
al., 2002). There, the one-dimensional case is considered
exclusively, i.e. concentrations of ligand and receptor that are independent
of y, even in the presence of a clone. At the boundaries x=0
and x=Lx, Lander et al. imposed the ligand
concentrations. In particular, at x=Lx the
concentration was fixed to A=0, which implies that all ligands that
reach x=Lx are instantaneously degraded. Such a
Dpp sink does not exist in the wing disc. This sink has a significant
influence on the shape of the gradient obtained in the calculations of Lander
et al., with Lx=100 µm, whereas the difference becomes
insignificant for Lx=200 µm (see Fig. S3C,D in the
supplementary material).
At x=0, the boundary conditions imposed by Lander et al. are also
problematic. These boundary conditions imply that at x=0 the ligand
concentration is imposed by the secreting cells but is unaffected by the
exchange of ligands between secreting and non-secreting cells via diffusion
(for details, see supplementary material). We refer to the boundary conditions
imposing the ligand concentration and the ligand current as `concentration
boundary conditions' (Lander et al.,
2002) and `current boundary conditions' (this work),
respectively.
We also performed one-dimensional calculations in the presence of a clone (Fig. 7A-C). In these calculations, the clone region is represented by an interval on the x-axis. We find that a one-dimensional description can generate ligand profiles that qualitatively correspond to the profiles in the x-direction of a two-dimensional calculation (Fig. 3C), if the extension of the clone in the y-direction is larger than the distance over which the gradient forms (compare Fig. 7C and 7D). For the present choice of parameters and an extension of the clone of 50 µm in y-direction, this criterion is satisfied. The contrast c of shadows in the two-dimensional geometry can be determined approximately in a one-dimensional calculation by taking the difference of the concentration behind the clone and the concentration at the same position in a calculation without a clone. In general, however, a two-dimensional description is required to describe the effects of the clone.
Transient versus permanent shadows
Our results show that the DBT model generates permanent shadows behind the
clone, whereas a DBTS model is able to generate transient shadows similar to
those observed in the experiments by Entchev et al.
(Entchev et al., 2000). Note,
that this finding differs from the results of Lander et al.
(Lander et al., 2002
), who
concluded that the DBT model can generate transient shadows.
In their one-dimensional calculations of the DBT model, like in ours, endocytosis block is modeled by a tenfold reduction of the internalization rates at t=0. However, in their study, the receptor concentrations [Rout] and [Rin] in the clone are simultaneously and abruptly set to the steady-state values corresponding to the reduced internalization rates. This assumption does not correspond to the experimental situation interpreted in the framework of the DBT model, because it would imply an instantaneous tenfold increase of the surface receptor concentration within the clone at the time of the temperature shift (see broken line in Fig. 7F). This is different from what is expected to happen in the experiment according to the DBT model: as the internalization rates in the clone are reduced in an abrupt fashion at t=0, the concentration of surface receptors only gradually increases (Fig. 7F, unbroken line). We have performed the same calculations as described in Lander et al., but changing the initial conditions for the receptor concentration (Fig. 7C). This one-dimensional calculation qualitatively leads to the same result as already discussed in two dimensions: a shadow develops that at t=5 hours is weak and becomes more pronounced after long time periods (compare Fig. 7C and 7D).
We have repeated the calculations of Lander et al., using the parameter values and system size, the boundary conditions, and the initial conditions chosen in their article. Note that in these calculations, we have set the initial surface receptor concentration in the clone to a tenfold larger value as compared with the remaining tissue as discussed above. As a result, we obtain ligand profiles that after long time periods exhibit a persistent shadow in the steady state identical to the situation in which the surface receptor level increases gradually (compare Fig. 7B and 7C). We found no transient shadows in these calculations. This result is different from the one published in their work (Fig. 7B).
The fact that these calculations lead to ligand profiles that differ from
those published in Lander et al. (Lander
et al., 2002) indicates a possible technical problem in their
calculations. Repeating the calculations of Lander et al., we noticed that
their results could be reproduced. However, this was possible only if the
receptor production rate inside the clone was reduced by a factor of 10 at
t=0 as compared with the one outside the clone. The results of our
calculations with this additional change in the clone are displayed in
Fig. 7A. In this case, the
surface receptor concentration in the clone after undergoing an initial
step-wise increase, relaxes to a steady-state value that is similar to the
steady state in the tissue outside the clone
(Fig. 7F, dotted line). The
corresponding ligand profiles of Fig.
7A indeed coincide with the results published in Lander et al.
(Lander et al., 2002
), see
Fig. 7 therein. It is possible
that in these calculations the receptor production rate in the clone was
reduced by a factor of 10. In summary, in the case of the calculations
discussed in Lander et al. (Lander et al.,
2002
), the shadow most likely appears because of the sudden
step-wise increase of the surface receptor level; the shadow disappears at 24
hours because the receptor production rate is reduced and the surface receptor
level therefore relaxes to approximately the same steady state as outside the
clone.
Our results emphasize the facts that the number of dimensions considered (in particular in the presence of mutant clone) (Figs 3, 4), the size of the AOI (see Fig. S3 in the supplementary material), the boundary conditions (in particular the `source boundary' and the `distal boundary') (Fig. 2), and the initial conditions (most notably the levels of surface receptor in the clone at the beginning of the experiment) (Fig. 7F) are of key importance.
Why the DBT/DBTS models fail to explain Dpp spreading
We have shown in this work that neither the DBT nor the DBTS model can
explain the observed ligand and receptor profiles during Dpp spreading in the
wing disc. Why should these models fail even though they incorporate many
essential phenomena such as ligand diffusion, internalization and resurfacing
via receptor recycling?
The essential point of both the DBT and the DBTS model is that ligand transport, which is described by the ligand current given in Eqn 1, is solely because of diffusion. In other words, this means that ligand bound to the surface receptors when internalized can only resurface at the same position on the cell surface where it was internalized. Only in this case is Eqn 1 justified and the intracellular transport of the ligand would not contribute to the current of the ligand in the tissue. This implies that simple reaction diffusion models ignore that in principle, ligand could also be transported by traveling through cells and resurface at other positions on the cell surface when receptors are recycled.
The fact that the DBT and DBTS models, which ignore these effects, cannot account for observed Dpp spreading suggests that contributions of receptor trafficking to transport and ligand current may indeed play an important role. We are currently generalizing the DBT/DBTS models to incorporate all relevant transport phenomena (diffusion and transcytosis) in the ligand current as well as the possibility of extracellular degradation of the ligand.
Interplay of diffusion and planar transcytosis: a working hypothesis for Dpp spreading
Our working hypothesis is that two phenomena contribute to the Dpp current
in the developing wing epithelium: extracellular diffusion and intracellular
trafficking (i.e. endocytosis plus resecretion). What is the relative
importance of these two phenomena to the spreading of the morphogen? Both
might be important. Limited by binding to the extracellular matrix and/or
degradation, extracellular transport of the morphogen may only account for the
spreading of the ligand across a few cell diameters. Intracellular trafficking
in turn accounts for the movement of the morphogen across one cell diameter.
Both phenomena together then lead to the long-range spreading of the
morphogen.
Although it is expected that extracellular diffusion plays a role during
morphogen spreading (Crick,
1970), it has been argued that extracellular diffusion alone is
insufficient to understand the reliability and precision of the formed
gradient (Kerszberg and Wolpert,
1998
). The important role of intracellular trafficking has been
uncovered in experiments in which endocytosis is blocked during morphogenetic
signaling (González-Gaitán,
2003
). When endocytosis is blocked in the receiving tissue, Dpp
spreading does occur, but generates a short-range gradient and thereby
signaling responses only within 3 to 5 cells
(Entchev et al., 2000
;
González-Gaitán and
Jäckle, 1999
). In particular, in a thermosensitive
alpha-adaptin mutant, Dpp activates transcription of its target gene
spalt only within 4-5 cells from the source
(González-Gaitán and
Jäckle, 1999
), instead of within 15 cells in WT. Similar
results where obtained by expressing a dominant-negative Rab5 mutant, which
impairs endocytosis and endosomal dynamics
(Entchev et al., 2000
). These
results do not exclude a role of endocytosis in the transduction, rather than
on the spreading of Dpp. However, in the `shibire rescue assay', the reduced
range of the extracellular Dpp gradient
(Fig. 6D,E) indicates that
impaired endocytosis restricts the spreading of Dpp.
This report is a theoretical and experimental study to address whether
diffusion as the sole transport mechanism can explain the spreading of Dpp. We
are currently studying the role of different transport mechanisms for Dpp
spreading. Based on the values given in
Table 1, it has been argued
that the rates of endocytosis and recycling known for the EGF receptor in
cultured cells are too small to allow for a sufficiently rapid transport by
transcytosis (Lander et al.,
2002). Indeed, our first results based on generalized models
(including diffusion and transport by planar transcytosis) show that the
parameter values used in this work (Table
1) do not produce consistent gradients during reasonable times. In
particular, these models require a faster rate of endocytosis and recycling
than those known for the EGF receptor in cultured cells. Therefore, it is
essential to measure directly the different dynamic parameters, including the
extracellular diffusion coefficient as well as the rates of endocytosis,
degradation and recycling of Dpp in the developing wing. To estimate these
parameters in situ we are currently monitoring photoactivatable fusion
proteins in different cellular locations (extracellular versus endosomal) in
the very context of the developing wing epithelium.
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ACKNOWLEDGMENTS |
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Footnotes |
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Supplementary material for this article is available at http://dev.biologists.org/cgi/content/full/131/19/4843/DC1
* These authors contributed equally to this work
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