© 2019. Published by The Company of Biologists Ltd | Development (2019) 146, dev176933. doi:10.1242/dev.176933
RESEARCH ARTICLE
Dynamic Hh signalling can generate temporal information during
tissue patterning
ABSTRACT
The differentiation of tissues and organs requires that cells exchange
information in space and time. Spatial information is often conveyed by
morphogens: molecules that disperse across receiving cells to generate
signalling gradients. Cells translate such concentration gradients into
space-dependent patterns of gene expression and cellular behaviour. But
could morphogen gradients also convey developmental time? Here, by
investigating the developmental role of Hh on a component of the
Drosophila visual system, the ocellar retina, we have discovered that
ocellar cells use the non-linear gradient of Hh as a temporal cue,
collectively performing the biological equivalent of a mathematical
logarithmic transformation. In this way, a morphogen diffusing from a
non-moving source is decoded as a wave of differentiating photoreceptors
that travels at constant speed throughout the retinal epithelium.
KEY WORDS: Drosophila, Hedgehog, Patterning, Systems
modelling, Visual system
INTRODUCTION
Morphogens of the hedgehog (hh)/Shh family contribute spatial
information during the development of a wide range of organs
and organisms (Ingham et al., 2011; Briscoe and Thérond,
2013). Produced at specialized sites within developing organs, Hh
molecules disperse and receiving cells respond according to the
Hh concentration that reaches them. The mechanisms of Hh
dispersion are not yet fully understood, and include potential
transport in exovesicles or associated with specialized filopodia,
called cytonemes. The lipid modifications of Hh (by cholesterol and
palmitic acid) tether it to the membrane, ruling out free diffusion as
the major transport mechanism for Hh (reviewed by Simon et al.,
2016). In receiving cells, Hh molecules bind to membrane receptors
of the patched ( ptc) family. In Drosophila, the receptor Ptc (Nakano
et al., 1989) forms a receptor complex that also includes the
adhesion molecules iHog and Boi (Bilioni et al., 2013). Hh binding
to Ptc relieves the repression of Smoothened (Smo) by Ptc, which, in
turn, blocks the processing of the Gli transcription factor cubitus
interruptus (Ci) into its repressor form. The result of this doublenegative regulation is the stabilization and activation of full-length
Ci (CiA), which then acts as a transcriptional activator of Hh
pathway targets (Aza-Blanc et al., 1997; Alexandre et al., 1996).
1
CABD (CSIC-Universidad Pablo de Olavide-Junta de Andalucı́a), GEM-DMC2
Unit, Campus UPO, 41013 Seville, Spain. 2Instituto de Biologia Molecular e Celular/
i3S, Universidade do Porto, 4200-135 Porto, Portugal. 3Centro de Biologı́a
Molecular Severo Ochoa (CSIC-UAM), Campus de Cantoblanco, 28049 Madrid,
Spain.
*Authors for correspondence (fcasfer@upo.es; david.miguez@uam.es)
F.C., 0000-0002-2181-3858
Received 14 February 2019; Accepted 19 March 2019
One of the target genes activated by Hh is the receptor ptc itself
(Hidalgo and Ingham, 1990; Capdevila et al., 1994). Because Ptc is
simultaneously the Hh receptor and a positive target of the pathway,
it plays a very important dynamic role in Hh-driven patterning
processes. As the pathway is activated, Ptc expression rises
closest to the source (where higher Hh levels are received),
trapping increasing amounts of Hh. This mechanism allows the
reshaping of the Hh gradient as time passes, starting from shallower
longer-reaching gradients to steeper shorter-reaching ones. This
phenomenon has been observed both in Drosophila and vertebrate
systems, and is important in establishing dynamically different
domains of gene expression at different distances from the Hh
source (Gallet and Therond, 2005; Nahmad and Stathopoulos,
2009; Dessaud et al., 2007; Chamberlain et al., 2008).
However, and although Hh signalling has been mostly involved
in spatial patterning, in two systems Hh has also been shown
to be required for temporal patterning – i.e. the reiteration of a
developmental process at a particular pace. During the development
of the Drosophila compound eye, Hh drives a wave of photoreceptor
(R) cell differentiation across the eye primordium at a constant speed
(Ma et al., 1993; Heberlein et al., 1993). A similar Shh moving wave
has been described during the differentiation of the ganglion cells
in the zebrafish retina (Neumann and Nuesslein-Volhard, 2000).
However, these waves are not generated based on the morphogen
characteristics of Hh/Shh (i.e. differential responses to varying
Hh concentration in space), but on the fact that the source of Hh
production itself moves across the developing retina: Hh/Shh
molecules are expressed in differentiating retinal cells (R cells in
Drosophila and ganglion cells in zebrafish) and non-autonomously
induce progenitors to differentiate into retina cells that, in turn, start
producing Hh/Shh. In this way, the source of signalling molecule
moves coupled to the differentiation process.
In Drosophila, the compound eye develops from the cephalic disc
(also called the ‘eye-antennal’ disc), a monolayered epithelial sac
that additionally gives rise to another component of the fly visual
system: the ocellar complex. This complex comprises three small
camera-type eyes, or ocelli (one anterior ocellus and two posterior
ocelli), located on the forehead of the fly that are part of the visual
system of most insects (Fig. 1A,B). Similar to the compound eye,
the specification of the ocelli requires Hh signalling (Royet and
Finkelstein, 1996; Blanco et al., 2009; Aguilar-Hidalgo et al.,
2013). In the prospective ocellar complex region of the disc, one
domain of Hh expression is flanked by two regions competent to
differentiate into the ocellar photoreceptors (R cells) under the
action of Hh signalling. One marker of competence is the gene eyes
absent (eya) (Blanco et al., 2009; Aguilar-Hidalgo et al., 2013)
(Fig. 1C,D). When the two contralateral discs fuse, the anterior
ocellar regions merge into the single anterior ocellus (aOC), while
the two other regions remain separate and will develop into the
paired posterior ocelli ( pOC). Previous work has defined the gene
1
DEVELOPMENT
Diana Garcı́a-Morales1, Tomá s Navarro1, Antonella Iannini1, Paulo S. Pereira2, David G. Mı́guez3, *
and Fernando Casares1,*
RESEARCH ARTICLE
Development (2019) 146, dev176933. doi:10.1242/dev.176933
produced at a spatially static source, can be read as a ‘time arrow’
during R differentiation.
Fig. 1. Photoreceptor (R) differentiation in the Drosophila ocelli.
(A) Scanning electron microscope view of a Drosophila head. The ocelli
(oc), the compound eye (ce) (both pseudocoloured) and the antenna (a) are
outlined. (B) Confocal image of an eye-antennal head primordium of a
Hh:GFP-BAC larva (late third instar) marking the prospective ocelli,
compound eye and antenna. Hh:GFP is in green. (C) Higher-magnification
of the prospective ocellar region of a Hh:GFP-BAC primordium (green) stained
for Eya (competence marker, blue) and Elav (neural marker, magenta).
Hh is produced from a central domain that will become the interocellar
region (iOR). The position of the Hh-expressing domain is marked with
and asterisk in C-E’’’’. Adjacent to it, the anterior and posterior domains of
Eya-expressing cells will become the anterior (aOC) and posterior ( pOC)
ocelli, respectively. (D) Schematic representation of the ocellar region,
showing the Hh-producing and Eya-expressing domains. The arrows indicate
the spatial axes. (E-E’’’’) Temporal series of pOC regions from progressively
older larvae/early pupa (as indicated by the ‘time’ arrow), marked with Eya
(blue) and Elav (Elav>nRFP_ires_mGFP). Images are from different, fixed
discs. Elav-expressing photoreceptor (‘R’) cells appear first closest to the
Hh source (E) and then accumulate successively in more distal regions
(E’-E’’’’). Nuclei and membranes of Elav cells are marked in magenta
and green, respectively.
regulatory network that, under the control of Hh, results in the
specification of the OC competent regions and regulates their size
(Aguilar-Hidalgo et al., 2013, 2016). Here, we further investigate
the role of Hh in the next developmental step: the differentiation of
the ocellar retinas. First we find that, in the ocelli, R differentiation
also proceeds as a wave of constant speed, and that this wave
depends on Hh. However, and in contrast to the compound eye, Hh
is not expressed in ocellar R cells, but remains expressed in a
spatially static source. Our work further shows how the non-linear
gradient that emanates from this source of Hh signal can in principle
be translated into a wave of R differentiation with constant speed,
owing to a single modification in the Hh signalling pathway: the
attenuation of Ptc expression as R cells differentiate. Thus, Hh,
In order to study how Hh signalling controls the differentiation of
the ocellar retinas, we first set to study the dynamics of R cell
differentiation, focusing on the larger posterior ocellus.
The ocellar competent regions, which abut the Hh-expressing
domain, can be labelled with Eya, and R differentiation can be
followed using the neuronal markers Elav and Glass. In fixed discs
of increasing age, we observed that R cell differentiation proceeded
in a wave-like fashion – i.e. differentiation starts in the vicinity of the
Hh source and then progress in a proximal-distal direction across the
ocellar tissue (Fig. 1E). The transition from precursors to R cells can
be monitored using the precursor marker gene senseless (sens)
(Nolo et al., 2000) (Fig. 1, Fig. S1A-C). We find that, as in the
compound eye, Sens expression precedes temporally that of Elav.
Sens expression in differentiating R cells is transient, and it
decreases as Elav expression increases. Spatially, Sens and Elav
distribute along a proximal-distal axis with respect to the Hh source.
Therefore, the differentiation wave can be visualized as a succession
of Elav and Sens along this axis, with new Sens-expressing cells
being added progressively further away from the Hh source as
differentiating cells express Elav and downregulate Sens (Fig. 1,
Fig. S1). Importantly, and in contrast to the moving wave of Hh that
sweeps across the developing compound eye, Hh is never expressed
in ocellar R cells (Fig. 1, Fig. S1D,D′) (Aguilar-Hidalgo et al.,
2013; Amin et al., 1999). The Hh source remains the inter-ocellar
region and, therefore, does not move in space. To start investigating
the potential role of Hh signalling in organizing this wave, we first
examined the distribution of Hh across the competence domain,
which is about 40 μm (10 cells) wide, using a Hh:GFP BAC
construct (Chen et al., 2017). Hh:GFP disperses away from its
source following roughly a decaying exponential (Fig. 2A,A′ and
see below). The Hh receptor Patched (Ptc) is also a target of the
signalling pathway, so that its expression can be used as a read-out
of the signalling activity of the pathway (Nakano et al., 1989). We
found that, before R differentiation starts, Ptc expression follows the
Hh:GFP gradient (Fig. 2A,A′ and see below), indicating that Ptc
signalling intensity reflects Hh distribution across the ocellus. In
addition, this result suggested that the non-uniform Hh distribution
could contribute to generating the wave, transforming the spatial
gradient into a temporal axis, such that cells closer to the Hh source
(and therefore receiving a higher concentration of Hh) would
differentiate earlier than cells farther away. To test this possibility,
we equalized Hh signalling across the developing ocellus by
expressing, specifically in the ocellar primordia, uniform levels of
cubitus interuptus (ci), the Gli-type nuclear transducer of the Hh
pathway (Fig. 2B,C, Fig. S2A,B). As the stabilization of Ci depends
on Hh signalling (and this signalling decays as the distance from the
source increases), we drove expression of a mutant form of Ci that
cannot be phosphorylated by PKA (‘Ci-PKA’) and, hence, is not
cleaved into the repressive form of Ci (Methot and Basler, 2000). In
eyaL>Ci-PKA ocelli, a larger than normal number of cells had
initiated the expression of Sens and Elav relative to control ocelli,
indicating their premature differentiation. More importantly, the
progression of the wave seemed disrupted: instead of the succession
of Elav and Sens cells, Elav and Sens cells are intermingled in Cioverexpressing ocelli (Fig. 2B,C). This result was compatible with
the idea that the Hh signalling gradient encodes a temporal axis that
generates the wave-like differentiation of ocellar R cells. To test this
point more directly, we distorted the normal distribution of Hh by
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DEVELOPMENT
RESULTS AND DISCUSSION
RESEARCH ARTICLE
Development (2019) 146, dev176933. doi:10.1242/dev.176933
Fig. 2. Hh signalling and R differentiation wave. (A) Confocal image
of the ocellar region of a Hh:GFP; GMR>tdTomato (‘GMR>tom’) larva
(stage 17 ommatidia), stained for Hh:GFP (blue), Ptc (green) and
anti-Tomato (red). No R cells (‘GMR>tom’) have as yet differentiated.
(A′) Quantitative profiles of the Hh:GFP, Ptc and GMR signals across
the Hh-producing domain (shaded in grey) and the pOC (measured
in the dashed yellow box in A). Hh:GFP signal decays non-linearly.
Ptc signal follows that of Hh:GFP at this stage, when no R cell
(GMR>Tom) has yet differentiated. (B,C) pOC regions (boxed, like the
corresponding region in A) stained for Elav (blue) and Sens (red) of
discs from larvae of the same stage (21 ommatidia). In the control
(B, ‘eyaL>+’) a row of R-expressing Elav cells precedes a row of
Sens-expressing precursors. In eyaL>Ci-PKA (C, causing the uniform
expression of Ci), precocious differentiation is observed. In addition,
the differentiation wave, characterized by the succession Elav→Sens,
is broken. (D) Number of Elav-positive cells in the pOC (red) and
aOC (green) as a function of developmental time. The number of
ommatidial rows in the compound eye, which increases linearly with
time, was used as an internal developmental timer. Individual data
points (circles) and the means are represented and fit well to a line.
See Materials and Methods for a description of the statistical analysis.
Methods for a complete description of the statistical analysis).
We subjected the ocellar patterns of eyaL>Ci-PKA larvae to the
same analysis and found also that they were close to non-polarized
(Fig. S3E). These results confirm that, despite the variability of the
system, the pattern of differentiation from Sens precursors to Elav
photoreceptors progresses as a wave, and reinforce the notion that
the distribution of Hh across the developing ocellus is necessary for
organizing this wave.
Next, we tested whether blocking Hh signalling could result
in abrogation of R differentiation. To do that, we expressed a
dominant-negative Ptc receptor (PtcΔloop2), which, due to its
incapacity to bind Hh, represses the pathway constitutively (Briscoe
et al., 2001). Our results show that, as in the compound eye, Hh
is necessary for R differentiation in the ocelli (Fig. S2C-E).
Altogether, our results so far indicated that the time needed for a cell
to start differentiating depends on the amount of Hh that it receives.
Fig. 3. Altering Hh spatial distribution distorts
the differentiation wave. (A,B) Cartoon depiction
of the Hh sources (green domains) relative to the
retina-competent regions (blue) in control (A)
and wg>Hh (B) ocellar regions. The posterior
ocellus is marked as ‘pOC’. The green triangles
indicate the distribution of Hh from these sources.
In wg>Hh, Hh is expressed around the ocelli
and within the normal Hh expression domain.
(C) Late wg>Hh disc (stage 23) stained for GFP
(GFP:Hh), Sens and Elav. The boxed region
corresponds to that represented in A and B.
A′ and B′ are pOC regions from control and wg>Hh
individuals, respectively. (D,D′) Ocelli of control
(D) and wg>Hh (D′) adults. In wg>Hh, ocelli are
larger.
DEVELOPMENT
inducing new foci of Hh expression from around the developing
ocelli (wg2.11-GAL4; UAS-GFP:Hh or ‘wg>Hh’; Pereira et al.,
2006 and Fig. 3) to then compared the spatial patterns of Elav+Sens-,
Elav+Sens+ and Elav–Sens+ cells between control and wg>Hh ocelli
(Fig. 3A-D′). Because even the wild-type pattern shows some
variability, we used a statistical analysis to compare the ‘grouping’
(as measured by the departure from a random proportion of
neighbours of a given type) and ‘polarity’, which measures the
ordered succession of cell states along the proximodistal axis (and is
a defining trait of a wave) (Fig. S3A-C′). Control and wg>Hh
patterns were both significantly – but similarly – different from
random (Fig. S3D), as expected if spatially localized Hh drives the
pattern of differentiation. However, when ‘polarity’, the metrics that
reflects a wave-like organization, was analysed, control samples
were significantly more polarized than wg>Hh, which were
closer to a non-polarized distribution (Fig. S3E; see Materials and
3
Because Hh distribution decays non-linearly in space (Fig. 2A′),
R cells should also accumulate non-linearly over time (i.e. with
fast R cell generation close to the source and progressively slowing
down with increasing distance from it). To test this hypothesis,
we quantified the number of Elav-expressing R cells over
developmental time. As developmental timer, we used the number
of rows of ommatidia that have undergone differentiation in the
compound eye, which is known to increase at a constant speed
(Wartlick et al., 2014; Vollmer et al., 2016) at least during the second
half of the last larval stage (Spratford and Kumar, 2013), the period
during which ocellar differentiation takes place. In contrast with the
expectation, though, the number of Elav cells increased linearly with
time in both anterior and posterior ocelli, indicating that the
differentiation wave propagated at a constant speed (Fig. 2D).
In order to explore the signalling outputs in this system,
we constructed a mathematical model capturing the essence of the
Hh signalling pathway (see Materials and Methods). In this model,
Ptc represses Hh signalling targets unless it binds Hh. As Ptc is one of
the targets of the pathway, Hh binding to Ptc releases the repressive
action of Ptc and results in its upregulation (Nakano et al., 1989).
Sens is included as a target in the model, although this does not imply
that Sens is a direct target. Expression of Elav in Sens-expressing
precursors follows irreversibly, and to reflect the loss of Sens
expression observed in Elav cells, we have also included a
negative feedback from Elav to Sens (see Fig. 4A). The dynamics
of Hh production and dispersion in the model were calibrated
using measured Hh:GFP profiles determined experimentally
(Fig. S4; and see Table S1 for values, units and source of
parameters). The intrinsic variability of the system is modelled by
introducing a 20% variability in all parameters of the model (see
Materials and Methods). In brief, the model simulates a twodimensional array of 10×10 cells (see Fig. S5 and Movies 1 and 2)
that respond to an external concentration of Hh. Hh is being secreted
at one of boundaries of the system and diffuses through the array.
The response to Hh in each cell is simulated by numerically solving a
set of ordinary differential equations (ODEs) that model a simplified
version of the Hh signalling pathway (Fig. 4A, see Materials and
Methods). With no further assumptions, the model simulations
confirmed the prior expectation: the accumulation of Elav cells was
non-linear and differentiation was often not completed during the
developmental period allowed (40 h) (Fig. 4B). The fact that the
model was unable to reproduce the experimental observations
indicated that our understanding of the signalling dynamics was
missing some important process. Owing to the key relevance of Ptc as
both Hh receptor and target of the pathway, we examined in detail the
dynamics of Ptc accumulation during differentiation. We found that,
although before R cell differentiation Ptc signal followed a non-linear
decay with a strong peak close to the Hh source (see Fig. 2A,A′), at
later stages Ptc signal decreased dramatically in R cells, identified by
expression of Elav (Fig. 4C-D′). As binding of Hh to Ptc reduces its
mobility (Chen and Struhl, 1996), we reasoned that the reduction of
Ptc availability in R cells could allow the non-bound Hh to move over
these cells and disperse farther away from the source. In this model,
the sequential dampening of Ptc expression acts as a ‘desensitization’
mechanism. When this Ptc dampening was incorporated in the model
(simplified as a repressor link from Elav-R to Ptc) it now correctly
predicted that the differentiation wave moves with about constant
velocity, and achieves the full differentiation of the progenitor
population during the differentiation window (Fig. 4E) (see also
Movies 1 and 2). In addition, the simulated dynamic profile of Hh
matched that measured experimentally (Fig. S4), with its gradient
flattening and reaching further as developmental time progresses.
Development (2019) 146, dev176933. doi:10.1242/dev.176933
Fig. 4. Loss of Ptc in R cells suffices to explain linear differentiation
dynamics. (A) Cartoon diagram of the model for the Hh signalling pathway and
its downstream effects. (B,E) Spatio-temporal dynamics of the outputs of the
model without considering (B) or considering (E) a negative feedback from
Elav-expressing R cells to Ptc (‘E’ link in A). (B) R cells (blue) accumulate
hyperbolically and do not reach the end of the competent region within the
time frame of 50 h. (E) With negative feedback (all other parameters are
the same), R accumulation dynamics are close to linear and R differentiation
reaches the end of the competent region. Simulations have been carried
out, including a 50% reduction in Hh production rate along the 50 h time,
as observed experimentally. Similar results are obtained if this rate is constant
(Fig. S5). (C,D) Ocellar region of stage 18 (C,C′) and stage 23 (D,D′)
eyaL>GFP discs stained for GFP (marking the Eya-expressing competence
domain), Ptc and Elav (R cells). Axes are as in Fig. 1. Elav-expressing cells
(marked by arrows) show reduced levels of Ptc. Source code is available
in the supplementary material under source code File 1.
Simulations include the ∼50% reduction of Hh:GFP production that
we observed experimentally (Fig. S4A) but the results remain the
same if the Hh production rate is constant (Fig. S5). Therefore,
the desensitization of differentiating cells to Hh, caused by the
dampening of Ptc, would allow the field of ocellar competent cells to
transform the Hh gradient into a moving signalling and differentiation
wave of constant speed. It has been described that Ptc is
downregulated upon binding to Hh (Gallet and Therond, 2005;
Incardona et al., 2002; Torroja et al., 2004) and also in a selfregulated manner (Casali, 2010) in Drosophila wing discs. To test
whether the dramatic downregulation of Ptc we observed was due to
R cell differentiation or merely to a process depending on ligand
binding or Ptc concentration, we examined Ptc levels in the ocelli of
late discs from atonal (ato) mutant larvae, in which R differentiation
is abrogated (Fig. S6). For each disc, the levels of Ptc signal in the
ocelli were normalized relative to the signal in the antenna of the
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DEVELOPMENT
RESEARCH ARTICLE
RESEARCH ARTICLE
Development (2019) 146, dev176933. doi:10.1242/dev.176933
same disc. Whereas in control discs (ato1−/+) the relative levels of Ptc
decrease with time (Fig. S6A,B), Ptc expression is maintained at
levels comparable with those found in control discs before the onset
of R differentiation, despite their having been exposed to Hh for the
whole duration of the third larval stage (Fig. S6C). To test directly
whether R differentiation was causing Ptc downregulation, we drove
uniform and premature Sens expression to force ocellar cells to
differentiate prematurely. As expected, after Sens overexpression, the
ocellar region of eyaL>Sens larvae had an increased number of
Elav-expressing cells relative to stage-matched controls. These cells
also showed a concomitant loss of Ptc expression (Fig. S6F,G).
To investigate ptc regulation further, we analysed ptc expression
using a ptc-Z transcriptional reporter. Indeed, ptc-Z signal falls in
Elav-expressing cells, suggesting that, as differentiation proceeds, ptc
is repressed transcriptionally (Fig. S7). Therefore, in the ocelli, R
differentiation is a major controller of Ptc dynamics.
One important aspect of ocellar differentiation is that, by the end
of development, the number of R cells per ocellus is very consistent
(the number of R cells of the adult posterior ocellus is 47.9; s.d.=0.7;
n=5). However, we have noticed in static measurements of Hh:GFP
that its signal is highly variable (Fig. S4). To test for robustness, we
compared the output of the model with or without signal
desensitization, varying Hh production rates by up to 10%.
Although without desensitization the dynamics were far from
linear and the time to differentiation termination varied widely, the
model including reduced Ptc availability coupled with
differentiation maintained linearity (i.e. constant differentiation
speed) and showed low variability in time to termination, despite
these variations in production rates (Fig. 5, Fig. S8). Therefore, our
model predicts that, in addition to promoting a differentiation wave
of constant speed, the R differentiation-induced Ptc desensitization
results in increased developmental reliability.
Previous work had shown, in different developmental contexts,
how a spatially static source of Hh/Shh coupled to its intracellular
signalling network could generate spatial patterns of gene expression
(reviewed in Briscoe and Thérond, 2013). In all these cases, the
dynamics of Ptc expression were shown to be particularly important.
For example, in the Drosophila epidermis, Hh is produced in a stripe
per segment. Early, Hh spreads over the whole width of the segment
and represses the target gene Serrate (Ser). Later, as Ptc upregulation
sharpens the gradient, Ser becomes expressed in cells most distal to the
Hh source, with Ser cells contributing a specific cell type in the dorsal
epidermis. Interestingly, different segments exhibit different temporal
dynamics (with some segments never showing Ser expression)
(Gallet and Therond, 2005), suggesting that the Hh/Ptc dynamics may
be subject to the control of segment-specific Hox genes. Another
example is the patterning of the vertebrate neural tube along its dorsoventral axis by Shh, which is expressed in the floor plate. Here, the
upregulation of the receptor Ptc1 not only results in a change in the
signalling profile across the tissue, but also causes a progressive cellautonomous desensitization of the pathway, as increasing levels of
unbound Ptc1 inhibit the signal transduction pathway (Dessaud et al.,
2007). This desensitization may resemble the one we have described
here. However, in the ocellar retina, the pathway becomes desensitized
by a reduction of Ptc expression, which involves its transcriptional
downregulation in photoreceptor cells.
In this article, we show that a spatially static Hh source can also be
decoded as a linear ‘time arrow’ – a wave of differentiation of
5
DEVELOPMENT
Fig. 5. Robustness in the dynamics of the wave against changes
in Hh increases when Ptc feedback is present. (A,B) Space-time
plots when Hh concentration is increased and decreased by 10%
compared in the absence (A) or presence (B) of Ptc reduction in R
cells. Colours represent the expression levels of Ptc (green), Sens
(red) and Elav (blue). The solid line is used to represent the speed
of the wave as a guide to the eye. The intensity of Hh in the left panel
in A has been adjusted to facilitate comparison between A and B.
(C) Changes in the dynamics of the wave due to changes in Hh
concentration. The model with no Ptc reduction (blue dashed line)
is more sensitive to changes in Hh concentration than the situation
with Ptc reduction. Statistics performed using 30 independent
simulations for each point. Bars indicate the s.d. of each
measurement. (D) Schematic depiction of the model proposed.
Hh spreading leads to Ptc upregulation and maximal signal initially
closest to the source. As the cells differentiate, Ptc levels decrease,
allowing farther extension of Hh spreading. By each cell dynamically
responding to Hh, the ocellar primordium transforms a noisy
non-linearly decaying signal into a differentiation wave of constant
speed that is robust to signal noise. Source code for Hh signalling
model available in the supplementary material under source
code File 1.
photoreceptors with constant speed. This capacity requires a single
change in the regulation of the Hh receptor Ptc. Two system-level
properties are worth mentioning: First, the ‘log-transform’ of the
signal of the gradient is an active process, in the sense that cells are not
passive readers, but transform the signal dynamically through a
reactive intracellular signalling network. Second, the mathematical
transformation of the signal is an emerging property of the system:
although the signalling changes operate at the single cell level, this
transformation requires a number of cells coupled within a Hh
gradient. Even though the pervasive use of Hh/Shh as a morphogen
might be the result of evolutionary contingencies, an alternative
explanation is that Hh and its signalling pathway, by acting on fields of
cells, are flexible in the type of information outputs that cells generate
when reading the gradient. It is conceivable that this flexibility would
be a selective advantage that might have resulted in the Hh signalling
pathway being redeployed once and again during evolution.
MATERIALS AND METHODS
Drosophila strains and genetic manipulations
Hh:GFP (BAC) was used to monitor the expression for Hh protein (Chen
et al., 2017). ato1 is an atonal mutant allele (FlyBase) and ato:GFP has been
described by Quan et al. (2016). GAL4/UAS crosses were set up at 29°C to
maximize GAL4-driven expression, except when indicated. The hh-GAL4,
UAS-GFP:Hh strain was used as reporter for Hh expression (Callejo et al.,
2008). Elav-Gal4 (FlyBase) was used to drive UAS-H2B-mCherry-P2AeGFP-PH line (Sánchez-Higueras and Hombría, 2016) in differentiated R
cells, allowing the distinction between nuclei (mCherry) and cell
membranes (eGFP) (experiment at 25°C). The FlyLight (Jenett et al.,
2012) GAL4 line R20D09 from eya (herein referred to as EyaL-GAL4) was
used to drive UAS transgenes specifically in the anterior and posterior
ocellar competence domains (Fig. S2). UAS lines used were: UAS-nlsGFP
(FlyBase), UAS-Ci-PKA (Methot and Basler, 2000) and UAS-GFPptcΔloop2 (UAS-ptcDN) (Briscoe et al., 2001). Larvae from crosses of
eyaL-GAL4 and UAS lines were raised at 29°C. GMRtdTom was used as a
reporter of Glass to monitor the PR cells and membranes (Pappu et al.,
2011). Quantification of the number of R cells over time was performed in
the wild-type strain Oregon R at 25°C. To perturb the normal distribution of
Hh, a GFP-tagged Hh (UAS-GFP:Hh; Torroja et al., 2004) was driven with
the wg2.11-GAL4 strain (wg2.11-GAL4; UAS-GFP:Hh, or ‘wg>Hh’).
wg2.11 is an enhancer of the wg gene that is expressed surrounding the
ocellar region and overlapping the prospective interocellar region in the eye
imaginal disc [described by Pereira et al. (2006) and see Results].
Immunofluorescence
Medium to late third instar larvae and pupae were dissected and fixed
according to standard protocols. Immunostainings were performed as
previously described (Bessa and Casares, 2005). We used the following
primary antibodies: rabbit anti-GFP at 1:1000 (Molecular Probes), rat antiRFP at 1:500 (Chromotek), rabbit anti-β-gal at 1:1000 (Cappel), mouse antiEya 10H6 at 1:400, rat anti-Elav 7EBA10 at 1:1000 and mouse anti-Ptc at
1:100 were from the Developmental Studies Hybridoma Bank. Aliquots of
mouse anti-Sens at 1:250 were gifts from Andrew Jarman (University of
Edinburgh, UK), Bassem Hassan (ICM, Paris, France), Rosa Barrio
(Biogune, Leioa, Spain) and Xavier Franch (IBE-UPF, Barcelona, Spain),
and rat anti-Ci 2A1 at 1:5 was a gift from Bob Holmgren (Northwestern
University, Evanston, IL, USA). Imaging was carried out on Leica SP2, SPE
or SP5 confocal microscope.
Measurement of the Hh:GFP signalling gradient dynamics
Eye discs from the BAC Hh:GFP strain were dissected from 96-130 h after
egg laying (grown at 25°C) and stained simultaneously. Number of discs per
experiment was 11 or more and one representative example is shown.
Developmental stage was determined as number of ommatidial rows in the
region of the compound eye. Imaging was carried out using a Leica SP5
confocal setup with the same settings. Lasers were warmed up beforehand
for 1 h. Fluorescence intensity measurements were obtained with Fiji
Development (2019) 146, dev176933. doi:10.1242/dev.176933
(Schindelin et al., 2012) by selecting a ROI across the ocellar complex. Then
a Plot Profile was generated for the ROI and the quantitative data were
obtained were processed in Excel.
R cell recruitment over-time
Medium-late third instar OR-R larvae and pupae were dissected and stained
using anti-Elav antibodies to monitor the degree of differentiation from the
stage 17 ommatidia to stage 27 ommatidia. The total number of samples
quantified was 83 for both ocelli. Samples per time point ranged from five to
12. To analyse the correlation of the number of ocellar photoreceptors cells
(Rs) and developmental time, as measured by the number of ommatidia
rows in the compound eye, we performed an univariate linear regression,
using the formula:
Y ¼ b0 þ b1 X þ 1;
1 Nð0; s2 Þ,
where Y is the number of R cells, X is the number of ommatidial rows in the
compound eye; β0 is the intercept coefficient, β1 is the number of ommatidial
row coefficient, N is the number of data points and σ2 is the variance and ε is
the regression error. The model was estimated by the least squares method
using the lm() function in Rsoftware and validated checking for normality,
independence and homoscedasticity of residuals. The analysis shows a
statistically significant linear dependence between PR cell number and
developmental time, either when considering PR cell number of the anterior
or the posterior ocelli individually or aggregating the data from both ocelli.
Table 1 provides a summary of the statistical results of the linear regression.
Quantification of adult ocelli R cell number
Brain preparations, with the ocelli attached, were dissected from newly
hatched (0-1 days) adults, stained with anti-Elav and counterstained with
rhodamine-phalloidin (cell membranes) and DAPI (nuclei). Ocelli were
imaged as z-stacks on an SPE Leica confocal setup and reconstructed using
Imaris (Bitplane) for quantification.
Spatial statistics of Elav and Sens pattern under normal and perturbed Hh
distribution
We imaged as confocal z-stacks ocellar regions stained for Sens and Elav
from control (Oregon-R strain; n=19) or wg2.11>GFP:Hh (n=18), over the
18-23 ommatidia stage. Three cell states can be observed – (1) [Sens−,
Elav+], (2) [Sens(weak), Elav(weak)] and (3) [Sens+, Elav−] – that
correspond to differentiating photoreceptors, the transition between
precursors and photoreceptors, and precursors, respectively. To obtain a
bidimensional description of the distribution of these cells types in the
tissue, we superimposed an orthogonal grid (ImageJ: Analyze>Tools>Grid)
on a maximal projection of the z-stack sections comprising all Sens and Elav
signals. The cell size of the grid is set to correspond approximately to the
size of the nucleus of the cell, so that, in general, there is only one nucleus
per cell of the grid. When a nucleus spans two or more cells in the grid, its
position is allocated to the cell of the grid where most of the signal is. Then, a
1, 2 or 3 is assigned to each grid cell according to its Sens and Elav signal. A
grid cell with no signal is assigned a ‘0’. The result is a two-dimensional
matrix of positions of the three states per sample (Fig. S3).
Statistical analysis of Elav and Sens expression patterns
In order to test the departure from a random pattern of Sens and Elav
expression, we defined two statistics: ‘grouping’ and ‘polarity’. Importantly,
the degree of polarization will tell whether the pattern is compatible with a
Table 1. R cell recruitment over time and parameters of the linear
regression
Coefficient estimated
Coefficient P-value
R-squared
Adjusted R-squared
Model P-value
pOC
aOC
pOC+aOC
2.8067
<2e-16
0.7722
0.7689
2.2E-16
1.039
2.39E-15
0.5995
0.5937
2.391E-15
3.8386
<2e-16
0.7794
0.7762
<2.2e-16
6
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Development (2019) 146, dev176933. doi:10.1242/dev.176933
pi ¼
si
,
ni
where si is the number of neighbours of a given type and ni is the total
number of neighbours [this number will depend on the position of the cell
within the matrix, with cells in the centre with more neighbours (8) than
those in the periphery]. Grouping is a global property of the ocellus, so the
estimation of grouping for the whole ocellus could be reduce to count
the number of Elav- or Sens-expressing cells relative to total cells in the
neighbourhood:
P
si
P ¼ Pi
i ni
However, this grouping is strictly dependent on the proportion of Elav or
Sens in the ocellus, so in order to obtain an unbiased measure of grouping,
the total proportion of cells expressing a factor needs to be subtracted from
the proportion of this factor in the neighbourhood. As a correction of the
statistic thus defined we actually consider the total proportion as:
S1
N 1
Where S is the total number of cells expressing the factor in the ocellus and N
the total number of cells in it. We have to subtract 1 from the numerator and
denominator because each time we calculate the proportion of neighbours,
we focus non-randomly on a cell expressing the factor (effectively we are
‘removing’ one case from the sample) so the proportion of success in the
neighbourhood that can be expected in a random matrix would be lower than
the actual proportion. Grouping of cells of the same type is the expressed as
follows:
groupingðxÞ ¼ PðxÞ
Sx 1
,
N 1
where x is the expressed factor, Elav or Sens.
However, if we consider grouping of Elav around Sens or Sens around
Elav, then making the previous correction is not needed because this time
the expected proportion of success in the neighbourhood in a random matrix
coincides with the total proportion in the ocellus. For the case of grouping of
cells of one type (y) around a cell of the other type (x), the grouping would
be defined as:
groupingðx; yÞ ¼ Pðx; yÞ
Sy
N
Where x is the expressed factor in a cell, and y is the other factor, expressed in
the neighbourhood of the cell.
‘Polarity’ measures the ordered succession of cells states along a spatial
axis. In our case, it is the ‘proximodistal’ axis with ‘proximal’ defined as the
position closest to the endogenous Hh source. For each matrix and each
factor, it is possible to define a dichotomous response variable Y that
classifies a cell as expressing a factor, 1, or not, 0. So we can define a logistic
regression model to predict the expression of this factor in a cell using
column position X as a predictor:
~ 0 þ b1 X
LogitðY Þb
The hypothesis for Elav is that its expression will be ‘proximal’, i.e. the left
or first column, whereas Sens will be ‘distal’, i.e. the right or last column, so
after the estimation of the model for each factor, we will use these models to
predict the probability of finding ELAV in the first column and Senseless in
the last one. The following expressions define them:
If a ¼ Elav
PolarðaÞ ¼ PðY ¼ 1jX ¼ 1Þ
If a ¼ Sens
PolarðaÞ ¼ PðY ¼ 1jX ¼ nÞ,
and
where n is number of columns in the matrix and α is the factor used.
This probability has to be compared with the probability of finding
expression of α at that column randomly or, what is the same, with no
predictor used, which coincides again with the total proportion of the factor
in the matrix. Polarity is then defined as follows:
PolarityðaÞ ¼ PolarðaÞ
Sa
N
Where Sα is the number of cells expressing the factor and N the number of
cells in the matrix.
To carry out group comparison, for each matrix four measures of
‘grouping’ and two of ‘polarity’ were estimated:
groupingðElavÞ; groupingðSensÞ; groupingðElav; SensÞ;
groupingðSens; ElavÞPolarityðElavÞ; and PolarityðSensÞ
:
Then they were calculated for every matrix and plotted (Fig. S3). In order
to test for significant grouping differences between control and wg>Hh, a
Welch’s test for unequal variances was performed for each grouping
variable:
H0 : m1 ¼ m2
:
H1 : m1 = m2
As we aimed at testing whether there was a pattern of Elav and Sens
expression, we had to check that they were not distributed randomly, so
grouping should be larger than 0. Student’s t-test for each grouping
distribution and experimental group, control or wg>Hh, was performed:
H0 : m 0
:
H1 : m . 0
The same hypothesis was posed and the same test performed for polarity,
first to check whether these groups were significantly different from one
another and then to check whether the polarity was larger than 0.
Statistics and data treatment were performed in R software. Data matrices
were imported to R from.csv.
Adult cuticles dissections
The dorsal head capsules were dissected in PBS. Brain tissues and proboscis
were removed from the samples. All the structures were incubated overnight
in Hoyer’s:Lactic Acid (1:1) solution at 80°C (Magri et al., 2018). Imaging
was carried out on a Leica DM500B microscope with a Leica DFC490
digital camera. All images were processed with Fiji (Schindelin et al., 2012).
Modelling the Hh pathway in the Drosophila ocelli
Simulations were performed using an in-house computational script
developed in Matlab (The Mathworks). This script is available as source
code (Source code File 1). Equations are discretized in space and time using
an Euler approach, with adimensional concentrations but dimensional
variables in space and time. The model is based on a hybrid approach that
combines partial differential equations (PDEs) solved in a continuous space
and ordinary differential equations (ODEs) that are solved in a discrete
space. The PDEs account for the diffusive extracellular signals, whereas
the ODEs account of the intracellular reactions. Cells are simulated as
two-dimensional regions in a hexagonal Voronoi diagram, with cell-to-cell
variability introduced as gamma-distributed values for each of the kinetic
constants of the reactions involved, with a standard deviation of 20% of the
mean value.
The equations define a simplified representation of the Hh signalling
pathway, illustrated in Fig. 3. Our model is based on the idea that the
differentiation of photoreceptors regulated by Hh is a dynamic process,
7
DEVELOPMENT
wave-like organization. For the analysis, each matrix comprising 1, 2 and 3
cell types (Elav+Sens−, Elav+Sens+ and Elav−Sens+, respectively) is split
into two matrices, one in which 2 is identified as 1 and another in which 2 is
identified as 3, because ‘2’ is expression of 1 and 3 in the same cell. This
allows a straightforward statistical analysis.
‘Grouping’ is defined as the departure from a random proportion of
neighbours of a given type for each cell expressing Elav or Sens. For each
cell i, the proportion of Elav- or Sens-expressing neighbours, pi, is
calculated as:
Development (2019) 146, dev176933. doi:10.1242/dev.176933
owing to the fact that the amount of Hh that each cell in the tissue receives
depends on time. To reduce free parameters and to try to obtain a simplified
model that includes only the basic interactions that are required to reproduce
the experimental observations, we have condensed all production and
degradation rates in two constants (see Table 1). In addition, we have
condensed all Hill coefficients in three constants. Free Hh degradation or
Elav downregulation are not included in the model equations, as they are not
relevant to the process studied by the model. The set of interactions that the
model takes into account are outlined in the following paragraphs.
Diffusion of the Hedgehog (Hh) morphogen
Hh is secreted by producing cells in the intervening region between the
anterior and posterior ocellar competent regions (‘Hh source’) and then
disperses, generating a concentration gradient. The mechanism by which Hh
disperses is not totally understood, and several studies propose that Hh
travels through cytonemes (Gradilla and Guerrero, 2013) as an alternative to
diffusion. Overall, the highly noisy spatiotemporal profile of Hh distribution
in the ocellus (Fig. 4-Fig. S1) can be fitted with a second degree polynomial
that decreases non-linearly when moving away from the Hh source. This
fitting is used as a guide to the eye to illustrate how the profile of Hh changes
in space and time, and to compare with the profiles derived from the model.
Our model simplifies the details of Hh transport as two-dimensional
diffusion. This approach successfully reproduces the experimental data of
shape and dynamics of the Hh profile (see Fig. S3). The equation that
governs Hh dynamics is:
2
@Hhðx; y; tÞ
@ Hhðx; y; tÞ @ 2 Hhðx; y; tÞ
¼D
þ
@t
@x2
@y2
ð1Þ
As cells in the ocelli do not produce Hh, there is no production term in
Eqn 1. Instead, our model approximates the Hh source as a continuous
supply of Hh at one of the boundaries of the ocellus. The experimental data
show that Hh expression by the Hh-producing cells, monitored by a Hh:GFP
BAC, gradually decreases to 50% of its initial values during the period
through which cell differentiation is taking place. This is introduced in our
model as a continuous reduction in the Hh production rate at the production
boundary to around 50% of its initial value. However, similar computational
results are obtained if the Hh production rate is maintained constant (see
Fig. S5). The modulation of Hh intensity is performed by setting a constant
reduction of the rate of Hh expression in each iteration of the model,
calculated to match a similar reduction in the rate of Hh at the source
equivalent to the one observed experimentally.
Binding of Hh to its receptor Ptc
Hh binds to its receptor Ptc irreversibly to form a complex (Ptc-Hh) (Gallet
and Therond, 2005; Incardona et al., 2002; Torroja et al., 2004), following
the scheme:
kHh
Hhi þ Ptci ! Hh Ptci ,
The amount of Hh that reaches a given cell in the population interacts with
the free form of its receptor, Ptc. In the absence of Hh, free Ptc acts,
indirectly through inhibition of the signal transducer Smo, as a repressor of
Hh signalling target genes. This repression is set in the model as sigmoidal
function of Ptc, with cooperativity m=3 (slightly higher or lower values of m
also reproduce the experimental results). As one of Hh targets is Ptc itself,
the sigmoidal repression is introduced in the equation corresponding to Ptc,
forming a direct negative-feedback loop. In addition, a constant degradation
of Ptc is introduced to ensure a dynamic equilibrium in its concentration.
Taking this into account, the dynamics of Ptc is described by the
following ODE:
@Ptci ðtÞ
ai Ami
¼
kHh Ptci ðtÞ Hhi ðtÞ
@t
Ptci ðtÞ þ Am
i
ð3Þ
This ODE equation is then solved continuously in time but discretely in
space, i.e. for each cell i in the population. The amount of Hh molecules
consumed by each cell i in each particular position is the subtracted from the
continuous spatial variable Hh in the corresponding position. The resulting
Hh profile is then computed at the next time step using Eqn 1.
bi Ptci ðtÞ Elavmi ðtÞ
,
m
Elavm
i ðtÞ þ Ci
ð4Þ
where α and ß corresponds to the rate constant for production and
degradation. A corresponds to the half maximal concentration of the
sigmoidal curve, and m sets the slope of the sigmoidal. The next term
accounts for the binding of Ptc and Hh, following Eqn 2.
The second version of the model includes a reduction of available (‘free’)
Ptc in terminally differentiated photoreceptors. This is simplified in the
model by adding the last term in Eqn 4 in the form of a Hill function
dependent on Elav, a marker of photoreceptor (‘R’) fate.
Expression of Senseless (Sens)
One of the relevant Hh signalling pathway targets (albeit likely indirect) is
senseless (Sens), a zinc-finger transcription factor required for ocellar
photoreceptor differentiation downstream of the proneural gene atonal
(Nolo et al., 2000; Frankfort et al., 2001). Our model described the
dynamics of expression of Sens by the following ODE:
@Sensi ðtÞ
ai Cim
Am
i
¼
bi Sensi ðtÞ,
m
m
m
@t
Ptci ðtÞ þ Ci Elavi ðtÞ þ Am
i
ð5Þ
where the expression of Sens is mediated by simple direct repression by Ptc,
where the half maximal concentration of the sigmoidal correspond to B. In
addition, we have observed that, during ocellar differentiation, Sens
expression is also lost in terminally differentiated photoreceptors. We
represent this loss of Sens expression in the models as a direct repression by
Elav in each cell i. To make this repression stronger than the repression by
Ptc, the second term is elevated again to m.
Differentiation into a terminal photoreceptor cell
The events downstream of Sens that result in a terminally differentiated
photoreceptor cells are also simplified in a single activation of the elav gene.
Its expression is assumed as directly proportional to the amount of Sens.
Therefore, the equation for the dynamics of Elav takes the form:
ð2Þ
where kHh corresponds to the affinity rate constant of the interaction. Hhi
corresponds to the amount of Hh that a given cell i is receiving, computed
at each time step as the average value of Hh over the whole cell area of cell i.
In this way, the continuous value of Hh computed in Eqn 1 is converted to a
discrete value for each cell in the population Hhi.. This value is then used to
compute the amount of Hh that binds to Ptc via Eqn 2, as an ODE that is
solved for each cell in the hexagonal lattice:
@Hhi ðtÞ
¼ kHh Ptci ðtÞ Hhi ðtÞ
@t
Expression of Ptc and binding to Hh
@Elavi ðtÞ
ai Sensmi ðtÞ
¼
m
@t
Sensm
i ðtÞ þ Bi
ð6Þ
Once the concentration of Elav reaches a given threshold value in a cell i, the
model assumes an irreversible transition to a differentiated photoreceptor.
Acknowledgements
We thank T. Kornberg (UCSF), C. Sá nchez-Higueras and J. C. G. Hombrı́a (CABD),
G. Struhl (Columbia University) and J. Culı́ (CBMSO) for fly strains; A. Jarman
(University of Edinburgh), R. Holmgren (Northwestern University), B. Hassan (ICM),
R. Barrio (Biogune), X. Franch (IBE-UPF) and I. Guerrero (CBMSO) for antibodies;
and the CABD ALMI platform for imaging and image analysis support.
Competing interests
The authors declare no competing or financial interests.
Author contributions
Conceptualization: D.G.M., F.C.; Methodology: D.G.-M., T.N.; Software: D.G.M.;
Formal analysis: T.N., D.G.M.; Investigation: D.G.-M., A.I., F.C.; Resources: P.S.P.;
8
DEVELOPMENT
RESEARCH ARTICLE
Data curation: D.G.-M., F.C.; Writing - original draft: D.G.M., F.C.; Writing - review &
editing: D.G.-M., T.N., D.G.M., F.C.; Visualization: D.G.-M., T.N., A.I., F.C.;
Supervision: F.C.; Project administration: F.C.; Funding acquisition: D.G.M., F.C.
Funding
Research was funded through grants BFU2015-66040-P and MDM-2016-0687
(to F.C.) and BFU2014-53299-P (to D.G.M.) from the Ministerio de Ciencia,
Innovació n y Universidades (Spain).
Supplementary information
Supplementary information available online at
http://dev.biologists.org/lookup/doi/10.1242/dev.176933.supplemental
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