2814 RESEARCH ARTICLE
Development 139, 2814-2820 (2012) doi:10.1242/dev.077669
© 2012. Published by The Company of Biologists Ltd
EGFR-dependent network interactions that pattern
Drosophila eggshell appendages
David S. A. Simakov1, Lily S. Cheung2, Len M. Pismen1 and Stanislav Y. Shvartsman2,*
SUMMARY
Similar to other organisms, Drosophila uses its Epidermal Growth Factor Receptor (EGFR) multiple times throughout development.
One crucial EGFR-dependent event is patterning of the follicular epithelium during oogenesis. In addition to providing inductive
cues necessary for body axes specification, patterning of the follicle cells initiates the formation of two respiratory eggshell
appendages. Each appendage is derived from a primordium comprising a patch of cells expressing broad (br) and an adjacent stripe
of cells expressing rhomboid (rho). Several mechanisms of eggshell patterning have been proposed in the past, but none of them
can explain the highly coordinated expression of br and rho. To address some of the outstanding issues in this system, we synthesized
the existing information into a revised mathematical model of follicle cell patterning. Based on the computational model analysis,
we propose that dorsal appendage primordia are established by sequential action of feed-forward loops and juxtacrine signals
activated by the gradient of EGFR signaling. The model describes pattern formation in a large number of mutants and points to
several unanswered questions related to the dynamic interaction of the EGFR and Notch pathways.
KEY WORDS: Feed-forward loop, Juxtacrine, Morphogen, Pattern formation
1
Department of Chemical Engineering, Technion-Israel Institute of Technology,
32000, Israel. 2Department of Chemical and Biological Engineering and Lewis-Sigler
Institute for Integrative Genomics, Princeton University, Washington Road,
Princeton, NJ 08540, USA.
*Author for correspondence ([email protected])
Accepted 17 May 2012
Several conceptual and mathematical models of eggshell
patterning have been proposed in the past (Wasserman and
Freeman, 1998; Shvartsman et al., 2002; Boyle and Berg, 2009;
Lembong et al., 2009; Zartman et al., 2011). Although some of
these models can explain the origin of the two-dimensional pattern
of br, none of them fully accounts for the highly coordinated
expression of br and rho. In particular, the connection between the
long-range gradient of EGFR activation by Grk and a single-cell
wide stripe of rho expression is unclear. To address this issue, we
synthesized the existing information into a revised model of follicle
cells patterning. Based on the computational analysis of this model,
we propose that rho expression is generated by sequential action of
feed-forward loops and juxtacrine signals set in motion by the Grk
gradient.
MATERIALS AND METHODS
Computational screen
In the computational screen for parameter values (Fig. 2D), a set of ODEs
(Eqns 1-5) was integrated for 10 dimensionless time units with zero initial
conditions for all variables. Juxtacrine signal arriving in a given cell is
given by arithmetic mean of stimuli (G5 values) in its neighbors in the
lattice. Grk distribution in the two-dimensional model was based on a
previously published model, adapted to Cartesian coordinates (Goentoro et
al., 2006; Zartman et al., 2011). To evaluate the inductive inputs
distribution (Fig. 3B), a reaction-diffusion problem given by Eqn 6 was
solved at steady state with appropriate boundary conditions (zero flux,
except for the anterior boundary for I2, where a unit flux is applied). A
standard finite elements method was used. The set of ODEs given by Eqns
1-5 (this time with two-dimensional inputs I1 and I2, as explained in the
Results) was integrated for 10 dimensionless time units with zero initial
conditions for all variables. Note that a separate set of equations is solved
for each cell on a hexagonal lattice, as each cell has its own pair of values
for I1 and I2.
In situ hybridization and immunohistochemistry
Description of the fluorescence in situ hybridization protocol and dpERK
staining are provided elsewhere (Fuchs et al., 2011; Zartman et al., 2009).
Digoxigenin- and biotin-labeled antisense probes were transcribed in vitro,
and purified with RNeasy mini kit (Qiagen). Primary antibodies used were
sheep anti-digoxigenin (3:500, Roche Applied Science), mouse anti-biotin
(1:100, Jackson ImmunoResearch) and rabbit anti-dpERK (1:100, Cell
DEVELOPMENT
INTRODUCTION
Epidermal Growth Factor Receptor (EGFR) regulates a multitude
of processes in development. Eyelid morphogenesis in mice and
feather array specification in chickens are just two examples from
a long list of developmental events that depend on EGFR signaling
(Atit et al., 2003; Mine et al., 2005). Some of the most advanced
studies of EGFR signaling have been carried out in Drosophila,
which, similar to other organisms, uses its EGFR pathway
throughout development (Shilo, 2003). Drosophila EGFR signaling
is involved in patterning of essentially all tissue types and
compartments in the embryo (Golembo et al., 1996; Szuts et al.,
1998; Yagi et al., 1998; Parker, 2006). In larval and pupal stages,
EGFR controls growth, patterning and morphogenesis of multiple
organs and structures, including wing veins and photoreceptor
arrays (de Celis, 2003; Roignant and Treisman, 2009).
During oogenesis, a gradient of EGFR activation patterns the
follicle cells, which form an epithelium over the developing oocyte
(Fig. 1A). This gradient is induced by Gurken (Grk), a TGF-like
ligand secreted from the oocyte (Schupbach, 1987; NeumanSilberberg and Schupbach, 1993; Neuman-Silberberg and Schupbach,
1994; Pai et al., 2000; Goentoro et al., 2006; Chang et al., 2008).
Patterning of the follicle cells provides inductive cues for body axes
specification in the early embryo and initiates the formation of two
respiratory eggshell appendages (Van Buskirk and Schupbach, 1999;
Roth, 2003). Each of the appendages is derived from a primordium
comprising a patch of ~55 cells expressing the transcription factor
broad (br) and an adjacent stripe of ~15 cells expressing rhomboid
(rho), a protease in the EGFR pathway (Berg, 2005; Ward and Berg,
2005). The br- and rho-expressing cells form the upper and the lower
parts of eggshell appendages, respectively (Fig. 1B-F).
Fig. 1. EGFR-dependent patterning of the follicle cells.
(A)Schematic of the egg chamber showing the localized source of Grk
secreted from the oocyte. A, P, D and V correspond to the anterior,
posterior, dorsal and ventral regions of the egg, respectively. (B)Spatial
pattern of grk mRNA. (C)EGFR controls gene expression through the
ERK/MAPK pathway. The image shows the spatial distribution of active
double-phosphorylated form of ERK (dpERK), visualized by the antibody
staining. (D,E)Fluorescent in situ hybridization images of br (D) and rho
(E) expression. Yellow arrowheads in B-E indicate the location of the
dorsal midline, corresponding to the highest levels of Grk. (F)Scanning
electron microscopy image of the eggshell, a proteinaceous structure
derived from the follicle cells. Each dorsal eggshell appendage is
formed by a primordium comprising br- and rho-expressing cells, which
form the top and bottom part of the appendage tube, respectively.
Signaling), followed by Alexa Fluor-conjugated secondary antibodies
(1:500, Molecular Probes). Confocal images were acquired using a Leica
SP5 confocal microscope, and processed with ImageJ (Rasband, US
National Institutes of Health, Bethesda, Maryland, USA, 1997-2011).
Eggshell images were obtained with a Hitachi TM-1000 table top scanning
electron microscope.
RESULTS
Description of the core mechanism
In this section we describe the network that can convert a graded
signal into an ordered arrangement of the expression domains of
three genes, similar to that observed during the patterning of the
follicle cells by EGFR (Fig. 2A,B). We start by considering a
row of cells, which can be thought of as a result of a cut along
the follicular epithelium (arrow, Fig. 2A). The lattice is presented
with a graded input, I, which models the Grk gradient (Fig. 2C).
The state of each cell in the lattice is characterized by expression
RESEARCH ARTICLE 2815
levels of five genes, G1-G5. G1 models a high threshold-target of
Grk, such as sprouty (sty) or pointed (pnt). G2 corresponds to
rho. G3, which corresponds to br, is activated by intermediate
levels of Grk. In addition to G1, G2 and G3, two more
components are needed to generate a configuration in which a
G2-expressing cell is positioned between broader expression
domains of G1 and G3 (Fig. 2C).
We attempted to derive the simplest network that may generate
the specific pattern of rho expression (Fig. 2A). G1, G2 and G3 are
essential components, which are well established by experiments.
G4 is required to reproduce the initial phases of rho expression
dynamics, of initially wide domain that later reduced to the ‘T’shaped domain. G5 is essential to generate the single cell-wide rows
of rho expression, as explained below.
The proposed regulatory network comprises several incoherent
feed-forward loops, network motifs in which an input activates both
the target gene and its repressor (Alon, 2006). First, an inductive
signal (I) activates G3 and its repressor, G1. Second, G3 represses G4,
which is activated by I. Third, G4 represses G2 and activates G5 that
in turn activates G2. Finally, the inductive signal I activates another
repressor of G3, G5. Regulatory interactions in this network can be
either cell-autonomous or juxtacrine, as denoted by solid and broken
lines in Fig. 2B, correspondingly. For cell-autonomous interactions,
the product of a given gene affects the state expression levels of other
genes in the same cell. For juxtacrine interactions, the effect is on the
nearest neighboring cells.
Some of the network interactions are deduced from experiments.
The feed-forward loop comprising I, G1 and G3 is based on the fact
that high levels of EGFR signaling activate both br and its
repressors (Morimoto et al., 1996; Deng and Bownes, 1997;
Boisclair Lachance et al., 2009; Zartman et al., 2009). As a result,
br is expressed only at intermediate levels of EGFR activation.
Second, Br (the protein product of G3 in the model) represses genes
such as Fas3, which, in the wild type, is expressed only at high
levels of EGFR signaling (Ward and Berg, 2005). This supports the
feed-forward loop formed by I, G4 and G3 that generates the
initially wide domain of G4 expression, which is later reduced to
the ‘T’-shaped domain.
The incoherent feed-forward loop composed of G4, G2 and G5
mimics the specific dynamics of rho expression, i.e. of initially
wide domain that is later refined to the ‘L’-shaped single cell-wide
rows. The product of G4 induces G5, which represses G3 and
activates G2 in the neighboring cells. This juxtacrine mechanism is
based on the fact that the Notch pathway, which commonly acts in
a juxtacrine mode, is active at this stage of oogenesis in the dorsal
midline (Ward et al., 2006). Furthermore, Notch signaling was
shown to repress br and activate rho (Ward et al., 2006). Based on
this, cell-autonomous loss of G3 in our model will lead to ectopic
expression of G4, which in turn will lead to ectopic expression of
G2. This is consistent with the results of experiments that
demonstrated that loss of br can lead to ectopic expression of rho
(Ward et al., 2006). Thus, the proposed network is largely
consistent with previous observations. To summarize, G1 represents
a high threshold EGFR target that represses br, G2 represents rho,
G3 represents br, G4 is a hypothetical component that is repressed
by br and induces G5, which models the Notch pathway.
We cannot formally prove that the proposed mechanism is the
simplest mechanism leading to the ordered arrangement of br- and
rho-expressing cells. At the same time, we could not come up with
a model that would have a smaller number of components or one
that would not involve sequential action of feed-forward and
juxtacrine loops.
DEVELOPMENT
Drosophila eggshell patterning
Development 139 (15)
dG 3k
+ ( I k − θ ) h − (G k − θ ) h − (0.5[G k −1
= h30
30
31
31 35
1
5
dτ
+ G 5k +1 ] − θ 35 ) − G 3k ,
Fig. 2. One-dimensional model and regulatory network.
(A)Fluorescent in situ hybridization image showing the expression of br
and rho. An L-shaped stripe of rho is located at the dorsal-anterior
boundary of the br expression domain. White arrow shows a cut across
this domain, which is used to construct a one-dimensional model of
follicle cells patterning. (B)Structure of the regulatory network. Cellautonomous and juxtacrine regulatory interactions are denoted by solid
and broken lines, respectively. Numbers above the arrows correspond
to the thresholds of seven out of nine gene regulation functions.
(C)Spatial distribution of the graded input (I) and qualitative expression
dynamics of three model variables (darker color corresponds to higher
expression level) used for selection of the values of two remaining
thresholds. (D)Computational selection of model parameters. All points
within the shaded region predict dynamics qualitatively similar to that
shown in C. (E)Spatiotemporal dynamics of all model variables for a
representative set of parameters selected within the shaded region in
D.
Mathematical model
In the one-dimensional model, the graded input follows an
exponential distribution: Iexp(–␾␨), where 0<␨<1 is a
dimensionless coordinate which spans 20 cells (Fig. 2C). The
expression levels of five genes in a given cell k are denoted by
G1k–G5k. For each of these variables, the dynamics is governed by
the sum of a linear degradation and a nonlinear generation function
describing the combined effects of regulatory signals.
dG1k
+ (I k − θ ) − G k ,
(1)
= h10
10
1
dτ
dG 2k
+ (0.5[G k −1 + G k +1 ] − θ ) h − (G k − θ ) − G k , (2)
= h25
25
24
24
4
2
5
5
dτ
(3)
dG 4k
+ ( I k − θ ) h − (G k − θ ) − G k ,
= h40
40
43
43
3
4
dτ
(4)
dG 5k
+ (G k − θ ) − G k .
= h54
54
4
5
dτ
(5)
In these equations, ␶ denotes dimensionless time. For simplicity,
we assumed that all species have the same decay rate. Following
previous models of gene regulation networks (Plahte, 2001;
Bolouri and Davidson, 2002; Albert and Othmer, 2003; Thieffry
and Sanchez, 2003; Longabaugh et al., 2005; Perkins et al., 2006),
gene expression is approximated by Heaviside functions. The
Heaviside function is equal to one when its argument is greater
than zero and is equal to zero otherwise. Thus, the rates of gene
expression in our model assume only two values, zero and
maximal. Switches in the rate of expression of a gene in a given
cell happens at particular thresholds denoted by ␪ij. In this notation,
i and j denote a target gene and its regulator, respectively (index 0
corresponds to the inductive input I).
For example, G4 is activated by the inductive input I and repressed
by G3. To describe this dual regulation, the rate of G4 production is
–
, where h+40 is a Heaviside function of the level of
given by h+40 . h43
–
is the
the inductive signal (I) minus the threshold (␪43), while h43
Heaviside function of the threshold (␪43) minus the level of G3. The
Heaviside function with superscript + is equal to one when its
argument is positive and zero otherwise, whereas the opposite is
correct for the Heaviside function with superscript –. Similar to our
earlier work on epithelial patterning (Pribyl et al., 2003; Reeves et
al., 2005), the effect of a graded input on a specific cell is given by
the integral of the input over this cell; Ik denotes integral for a cell k.
Selection of parameter values
To analyze the model, we needed to specify the values of its ten
parameters. We took advantage of previous studies of the Grk
gradient and published gene and protein expression images that
provide information about the spatial distribution of several model
components. First, based on the earlier estimates of the spatial
distribution of the Grk gradient, the length scale of the inductive
signal, denoted by ␾ in the model, is set to 3 (Goentoro et al., 2006).
This leaves nine parameters, corresponding to the thresholds of gene
regulation functions. As the input levels and values of all model
variables vary between zero and one, these thresholds also vary in
the same range. Importantly, most of the thresholds can be chosen
based on the experimentally observed gene expression patterns.
Based on the patterns of high threshold EGFR-target genes
(Morimoto et al., 1996; Yakoby et al., 2008a), we chose the G1
activation threshold in such a way that G1 is activated in three cells
corresponding to the high levels of the input. Given the distribution
of I, this leads to ␪100.65. Second, it is known that both rho and
br can be potentially expressed in the same cells, which correspond
to the intermediate levels of EGFR activation (Peri et al., 1999). In
our one-dimensional lattice, this corresponds to 11 cells (Fig. 2C).
Based on this, the activation thresholds of G3 (which models br)
and G4 (which activates G2, which in turn models rho) are given
by ␪30␪400.2.
The threshold of repression of G3 by G1 (br repression by Pnt)
is set to a low value, ␪310.1, ensuring that br is repressed without
a considerable delay following the induction of its repressor
DEVELOPMENT
2816 RESEARCH ARTICLE
(Yakoby et al., 2008b; Boisclair Lachance et al., 2009; Fuchs et al.,
2011). Similarly, the activation thresholds of G5 by G4, and G2 by
G5 are chosen to be low: ␪54␪250.1. This ensures that G2 is
initially expressed in the same cells as G3 and G4 (Peri et al., 1999).
In addition, repression of G2 by G4 is set to have a high threshold,
␪240.9, providing a delay of G2 repression in cells exposed to high
levels of inductive signal. This is based on the fact that rho is
initially expressed in a large region, overlapping the domains of its
repressors (Peri et al., 1999).
Selecting the values for the remaining two thresholds, ␪35 and
␪43, corresponding to repression of G4 by G3 and of G3 by G5 is
less straightforward. However, given the simplicity of the model
and low computational cost of solving it numerically, the values for
remaining two thresholds can be constrained computationally. To
do this, we solved the model for multiple pairs of ␪35 and ␪43,
chosen on a uniform grid (Fig. 2D), with all other parameters
selected as described above (Fig. 2B). For each of the resulting
solutions, we checked whether G2 is initially expressed in a domain
that overlaps the expression domains of G1 and G3, which is later
refined to a single cell located between the expression domains of
G1 and G3 (Fig. 2C). Following this procedure, we could identify
the values of ␪35 and ␪43 that satisfy these criteria (Fig. 2D).
Qualitative dynamics in one dimension
For each of the points inside the identified parameter region, the
time-dependent solution is qualitatively similar to the
representative examples shown in Fig. 2C,E. Initially, G1, which is
a high-threshold target of the inductive signal, is expressed in a
narrow region, while G2 and G3 are expressed in a wider domain.
The G2 expression domain is then refined by the repressive effects
of G3 and G4, while G4 is repressed by G3. Note that G4 is both a
repressor and an indirect activator of G2 (Fig. 2B).
In our model, the activating and repressive effects of G4 on G2
are separated in time, by setting low and high thresholds of
activation and repression, respectively. In cells where G4, which is
essential for G2 activation (via G5), is repressed by G3, G2 is also
repressed. This corresponds to the fact that late rho expression is
abolished in br-expressing cells (Peri et al., 1999). Thus, br is
repressed at the posterior border of cells expressing G5, which
models the effect of the Notch pathway. The juxtacrine repression
of G3 by G5 ensures that G3 is removed from cells expressing G2.
This agrees with the fact that br is not expressed in cells expressing
rho at late stages in the patterning process (Dorman et al., 2004;
Ward et al., 2006). In order to obtain the qualitative dynamics
represented by Fig. 2C,E, the repression of G3 by G5 should be
delayed, to ensure that G3 represses G4. This is reflected in Fig. 2D,
where a wider range of ␪43 is obtained for higher values of ␪35.
Note that G2 (rho) is induced next to cells inducing G5, which is
downstream of G4, which is in turn repressed by G3 (br). Thus, G2
is not induced in the G3-expressing cells. The formation of the
single-cell stripe of rho expression is a direct consequence of the
action of the incoherent feed-forward loop composed of G4, G5 and
G2. Initially, G2 is activated in the domain overlapping the
expression domain of G4 (note that G2 activation threshold is low).
G2 is then repressed by G4, but remains in the neighboring cell
(where G4 is not expressed), owing to the juxtacrine character of
the G2 activation by G5.
Importantly, the ordered arrangement of cell fates predicted by
the model, with a single G2-expressing cell, bounded by the wider
areas of cells expressing G1 and G3 (Fig. 2C,E), persists over a time
period that exceeds the decay constants of individual components
by at least an order of magnitude. We established that such
RESEARCH ARTICLE 2817
solutions are robust with respect to small perturbations of model
parameters, as long as the remaining seven thresholds satisfy
certain inequalities. For example, the activation threshold for G3
should be significantly lower than that for G1. Thus, our analysis
identified multiple parameter sets that generate the desired
arrangement of gene expression domains (Fig. 2C).
The ordered arrangement of gene expression domains in the
presented model is generated in a stepwise fashion, by sequentially
acting feed-forward loops and juxtacrine signaling. This
mechanism may control rho expression in the follicle cells. Indeed,
similar to G2 in our model, rho is initially expressed in a wide
domain induced by a long-range Grk gradient. Later, rho is
downregulated in the midline and lateral follicle cells, as well as
along the anterior boundary, with expression remaining only in two
stripes at the dorsal-anterior borders of br expression patches (Peri
et al., 1999). Importantly, according to our model, the repression of
G3 (br) by G5 (Notch) is not necessary to generate the single cellwide row of rho, but is needed only to abolish br from the rhoexpressing cells.
Pattern formation in two dimensions
With only a few modifications our model can be used to analyze
patterns in two dimensions, on a hexagonal lattice of cells (Fig. 3).
First, we modified the spatial distribution of the inductive signal
(now denoted by I1, Fig. 3C), making it two dimensional and
consistent with the earlier studies of the Grk gradient (Goentoro et
al., 2006). We approximate the dorsal-anterior part of the main
body follicular epithelium, where the relevant patterning events
take place, with the lateral surface of a cylinder, as it is
schematically shown in Fig. 3A. The I1 distribution is obtained then
by solving a steady-state reaction-diffusion equation (Eqn 6, i1.2
corresponds to I1 and I2) with zero-flux boundary conditions, with
␾13 and f1 representing a source function, which equals 1 in a
restricted cusp-like dorsal-anterior domain and 0 everywhere else
(Zartman et al., 2011). The resulting distribution is shown in Fig.
3B.
0 = ∇ 2 I i + φ 2i ( f i − I i ) .
(6)
In this equation, ␾1 is the ratio of the size of the domain and the
characteristic length scale of morphogen degradation.
Second, we added another inductive signal (denoted by I2),
which models anterior-to-posterior gradient of signaling by the Dpp
pathway (Fig. 3B). This gradient is short ranged and is generated
by anteriorly secreted ligand. The distribution is obtained by
solving Eqn 6 with ␾214, f20 and a unit flux ( f1–—I21) along the
left (anterior) boundary of the computation domain. Earlier studies
established that Dpp represses br (Yakoby et al., 2008b). In our
model, this corresponds to repression of G3 by I2 (Fig. 3C). Finally,
based on our recent experiments, we restricted the patterning
effects of the dorsoventral inductive signal (I1) to the anterior
region of the system (Zartman et al., 2011). The nature of this prepatterning effect is still unclear, but it is possible that it results from
the earlier phase of EGFR signaling, before the anterior migration
of the oocyte nucleus (González-Reyes and St Johnston, 1998;
Nilson and Schupbach, 1999).
Adding these effects to the mathematical model requires
specifying the threshold of G3 repression by I2 and the size of the
anterior domain within which I1 can induce its target genes. Based
on the wild-type expression patterns of br and rho, we selected
these parameters in such a way that G3 is repressed in the
anteriormost two rows of cells by I2 and the inductive effect of I1
is restricted to the anterior part of the computational domain.
DEVELOPMENT
Drosophila eggshell patterning
2818 RESEARCH ARTICLE
Development 139 (15)
With these modifications, our model was able to provide a
quantitative description of wild-type dynamics of expression of pnt
(G1), rho (G2) and br (G3) in two dimensions (Fig. 3D,E, where G4
and G5 are also shown for clarity). The notable feature of the
simulated patterns is the formation of two L-shaped single cellwide patches of rho expression (Fig. 3D,E). Thus, parameter sets
identified for a one-dimensional model predict the dynamics of
two-dimensional pattern formation.
Analysis of mutants
Given a ‘wild-type’ parameter set, one can readily explore pattern
formation in mutant backgrounds. As an example, we provide
computational predictions of br and rho patterns in mutants with
altered distribution of Grk (Schupbach, 1987; Price et al., 1989).
As was shown earlier, increasing the level of Grk increases the
separation between the two patches of br (Deng and Bownes,
1997). At the same time, below a crucial value for the amplitude
of the Grk gradient, the patches of br expression fuse into one
(Deng and Bownes, 1997; Lembong et al., 2009). Furthermore, in
a mutant with a delocalized Grk, dorsally located patches of br
expand to the ventral follicle cells, generating an anterior ring of
br expression (Ward and Berg, 2005). Importantly, in all of these
backgrounds, the expression of rho is always located at the dorsalanterior border of the br domain and maintains its single cell width
(Neuman-Silberberg and Schupbach, 1994).
All of these effects are correctly predicted by our model and are
direct consequence of the proposed mechanism in which br plays an
active role in shaping the pattern of rho expression (Fig. 4Aa-d).
These are just a few from a long list of predicted patterning defects
that can be directly compared with a long list of experimental
observations. For example, in the absence of the anterior
prepatterning signal (I2) expression of G3 expands anteriorly (Fig.
4Ae). This is accompanied by the loss of the anteriormost part of G2
expression domain, in agreement with the effect of loss of Dpp on
the expression of br and rho (Yakoby et al., 2008b).
Our computational model can be readily used to predict the
results of experiments with genetic mosaics, whereby a component
of the network is perturbed in an arbitrarily chosen group of cells.
Several examples of computational mosaics are shown in Fig. 4B,
where we modeled the effects of inactivating the Notch pathway
(motivated by experiments by Ward et al., 2006), ectopic high
levels of EGFR signaling (motivated by experiments by Pai et al.,
DEVELOPMENT
Fig. 3. Two-dimensional pattern formation.
(A)Approximating geometry: the main body follicular
epithelium, which covers the surface of an ellipsoid, is
approximated by the lateral surface of a cylinder.
(B)Spatial distribution of inductive inputs I1 and I2,
which correspond to the Grk and Dpp gradients,
respectively. (C)Regulatory network, with the addition
of G3 repression by I2. (D)Two-dimensional dynamics
of G1-G5 expression predicted by the model, shown
for three points in time, indicated by arrows in E.
(E)Dynamics along a one-dimensional cut through the
domain shown by arrows in D. Compare with plots in
Fig. 2E.
Fig. 4. Computational prediction of br and rho expression in the
wild-type and mutant backgrounds. (A)Arranged from left to right
are the merged br and rho patterns for the wild type (a), patterns
computed when the doubled and halved amplitude of the Grk gradient
(I1) (b and c, respectively), patterns computed with delocalized Grk
gradient (d), and patterns computed in the absence of Dpp represented
by I2 in our model (e). (B)Arranged from left to right are the merged
br/rho patterns in the computational experiments approximating the
effects of genetic mosaics. In all examples shown, the group of mutant
cells is enclosed by black solid line. Notch loss of function (a) was
modeled by eliminating the juxtacrine connections in the regulatory
scheme in Fig. 3C (activation of G2 and repression of G3 by G5), by
–
setting h+250 and h35
0 in Eqns 2 and 3, respectively. EGFR
overexpression in mutant cells (b) was modeled by setting I1 above the
activation threshold of G1 in these cells. Loss of function of pnt and br
(c and d) was modeled by removing G1 and G3, respectively, in mutant
cells, by setting h+100 and h+300 in Eqns 1 and 3 for these cells.
2000), as well as the effects of pnt and br loss-of-function clones
(Zartman et al., 2009; Ward et al., 2006). Thus, we see that loss of
Notch signaling in the model leads to loss of rho and ectopic
expression of br in the same cells (Fig. 4Ba). The effect is confined
to the anterior part of the Notch clone and leads to ectopic
expression of br in a single row of cells, consistent with the fact
that br is also repressed by G1, which is expressed in the midline
and independently of Notch. At the same time, a patch of cells with
higher level of EGFR signaling can split the dorsal appendage
primordium in two smaller domains, with rho-expressing cells
located at the border of br-expressing domains (Fig. 4Bb). This
result is consistent with ectopic dorsal appendages that were
observed in response to generation of clones of cells hypersensitive
to EGFR signaling (Pai et al., 2000). In another example, a
midline-located clone of cells lacking pnt leads to ectopic br
expression and an associated rho border (Zartman et al., 2009;
Boisclair-Lachance et al., 2009). Finally, loss of br in the model
leads to ectopic rho expression, but only in a subset of cells that
lack br. Within the framework of our model, this reflects the effects
of G4, which is de-repressed in the absence of br. These
computational results demonstrate how the proposed model may
be used to summarize the existing experimental observations and
to predict spatiotemporal dynamics in a complex regulatory system.
Testing these predictions requires future experimental studies of the
dynamic interaction of the EGFR and Notch signaling pathways.
RESEARCH ARTICLE 2819
DISCUSSION
Previous studies of Drosophila oogenesis characterized the gradient
of EGFR activation by Grk, identified many of its transcriptional
targets, and began to assemble the regulatory network converting
EGFR signaling to complex gene expression patterns (Cheung et
al., 2011). A key feature in the emerging eggshell patterning
network is an incoherent feed-forward loop. This is the mechanism
by which a single-peaked gradient of EGFR activation by Grk
gives rise to the two-domain expression pattern of br. Cascades of
cell-autonomous feed-forward loops can establish patterns of
progressively increasing complexity, in which the expression
domains of multiple genes are arranged in a specific order.
However, cell-autonomous mechanisms cannot readily account for
the emergence of fine-grained patterns, such as the pattern of rho.
Studies by Celeste Berg and colleagues suggested that, in
addition to cell-autonomous mechanisms, rho is regulated by
juxtacrine signaling, mediated by the Notch pathway (Ward et al.,
2006). These studies suggest that the border of the Notch pathway
activation represses br. Furthermore, it has been shown that loss of
br leads to ectopic expression of rho. Here, we incorporate these
observations into a feed-forward model of pattern formation by the
Grk gradient and demonstrate that the combined mechanism can
indeed account for the wild-type patterns of br and rho and for
changes of these patterns in response to genetic perturbations.
Our model is based on the switch-like description of gene
regulation, commonly used in computational studies of gene
regulatory networks (e.g. Longabaugh et al., 2005; Perkins et al.,
2006). The main parameters in this model are thresholds in gene
regulation functions. We demonstrated that most of these thresholds
can be estimated based on the qualitative analysis of experimental
gene expression patterns, e.g. the size of the br domain and its
relation to the length scale of the Grk gradient (Goentoro et al.,
2006). The remaining parameters can be estimated based on the
numerical solution of the model and qualitative comparison of the
computationally predicted and experimentally observed patterns.
We provided a detailed description of this process, which starts
with the analysis of a simple one-dimensional model and ends with
the analysis of two-dimensional patterns in the wild-type and
mutant backgrounds.
Although our model is based on a number of established
components and interactions, some of them remain to be
established experimentally. Hypothesized components and
interactions may be revealed by studies of the regulatory regions
of br and rho, the outputs of the analyzed network (Cheung et al.,
2011). Experiments aimed at the identification of these regulatory
regions are currently under way in our group (Fuchs et al., 2012).
Future studies of these regions and their control by signaling
pathways will provide crucial tests of the model and are likely to
shed light on the mechanisms responsible for diversification of
Drosophila eggshell morphologies (Hinton, 1981; Kambysellis et
al., 1995; James and Berg, 2003; Nakamura and Matsuno, 2003;
Nakamura et al., 2007; Kagesawa et al., 2008).
Acknowledgements
We thank Celeste Berg, Jitendra Kanodia, Cyrill Muratov, Laura Nilson, Miriam
Osterfield, Trudi Schüpbach, Nir Yakoby and Jeremy Zartman for helpful
discussions.
Funding
This work was supported by the Human Frontiers Science Program
[RGP0052/2009-C].
Competing interests statement
The authors declare no competing financial interests.
DEVELOPMENT
Drosophila eggshell patterning
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