Mechanical Control of Morphogenesis by Fat/Dachsous/Four-Jointed Planar Cell Polarity Pathway

Abstract

The Right Move
During development, epithelial tissues deform to give rise to functional tissues and organs. How gene expression controls local cell mechanical properties to drive tissue deformation remains poorly understood. Bosveld et al. (p. 724 , published online 12 April) have uncovered how the conserved Fat/Dachsous/Four-jointed signaling pathway controls local mechanical cell properties to generate global tissue contraction in Drosophila epithelial tissue.

Full text

diffusion coefficients of the fusion proteins by
fitting a three-dimensional diffusion model to
recovery profiles (text S6 and figs. S19 to S21).
We obtained effective diffusion coefficients of
0.7 T0.2 mm
2
/s for Cyclops-GFP, 3.2 T0.5 mm
2
/s
for Squint-GFP, 11.1 T0.6 mm
2
/s for Lefty1-GFP,
and 18.9 T3.0 mm
2
/s for Lefty2-GFP (Fig. 4B,
figs. S18 to S23, and text S6). Thus, increased pro-
tein diffusivities reflect increased ranges, indicating
that differential diffusivity is a major contributor
to the differences in Nodal and Lefty range.
To test whether the experimentally determined
values for diffusivity and clearance accurately
predict the measured distribution profiles, we nu-
merically simulated signal secretion from a local-
ized source, diffusion, and clearance (12,14,26)
in a three-dimensional geometry appropriate for
blastula embryos (text S7). Using the measured
values for diffusivity and clearance, these simu-
lations yielded distribution profiles similar to the
experimentally determined protein distributions
(fig. S26) and thus provided independent support
for the validity of the experimental approaches.
Our results have two major implications.
First, differential diffusivity underlies differences
in activator/inhibitor range. The differences in
range (Cyclops < Squint < Lefty1 < Lefty2) are
reflected in the differences in effective diffu-
sion coefficients (Cyclops < Squint < Lefty1 <
Lefty2). There is a similar trend in half-lives,
but the differences in diffusivity are much more
pronounced than the differences in clearance.
During embryogenesis, the sources of Nodal
and Lefty overlap, but Nodal signaling is active
near the source and is inhibited by Lefty farther
away. Our results suggest that the lower mobil-
ity of Nodal allows its accumulation close to
the site of secretion, whereas the high mobility
of Lefty leads to rapid long-range dispersal and
prevents accumulation near the source. Thus,
the differential diffusivity of Nodal and Lefty
signals serves as the biophysical basis for the
spatially restricted induction of cell fates during
embryogenesis.
Second, the previously described network
topology of the Nodal/Lefty system and the
biophysical properties of Nodals and Leftys
measured here support the activator/inhibitor
reaction-diffusion model of morphogenesis: A
less diffusive activator (Nodal) induces both its
own production and that of a more diffusive
inhibitor (Lefty) (3,4). The Nodal/Lefty reaction-
diffusion system is further constrained by pre-
patterns and rapid cell fate specification; thus,
the system results in graded pathway activation
during mesendoderm induction and exclusive
pathway activation on the left during left-right
specification (see text S2 for detailed discus-
sion). Mathematical models have postulated that
the inhibitor in reaction-diffusion systems must
have a higher diffusion coefficient than the ac-
tivator. Several models suggest that clearance-
normalized inhibitor and activator diffusion
coefficients differ by a factor of at least 6, that is,
ℜ=(D/k
1
)
inhibitor
/(D/k
1
)
activator
>6(8,16,27–29).
The average ratio of the normalized diffusivities
of Leftys and Nodals measured here is ℜ≈14,
providing biophysical support for these modeling
studies (see text S8 for comparison of reaction-
diffusion systems). The different diffusivities in
the Nodal/Lefty biological system have counter-
parts in chemical reaction-diffusion systems. For
example, patterns can be generated in a starch-
loaded gel by combining an activator (iodide)
with an inhibitor (chlorite) in the presence of
malonic acid (30). In this in vitro system, diffu-
sion of the activator is hindered by binding to
the starch matrix and is thought to result in a
higher (factor of ~15) diffusivity of the inhibitor.
These models and our measurements raise the
possibility that differential binding interactions
and a ratio of at least a factor of 5 to 15 of inhib-
itor and activator diffusivities might be a general
feature of reaction-diffusion–based patterning.
References and Notes
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Acknowledgments: We thank X. Zha ng for help wi th the
cloning of Cyc lops constru cts, H. Othmer and A. Lander for
helpful discussions, J. D ubrulle for discussions and primers
for quantitat ive reverse transcription polymerase chain
reaction, and S. Mango for comments on the manuscript.
Supported by European Molecular Bio logy Organi zation and
Human Frontier Science Program (HFSP) Long-Term
Fellowships (P.M.), the NSF Graduate Research Fellowship
Program (K.W.R.), NIH gran t 5RO1GM56211, and HFSP gran t
RGP0066/2004-C.
Supplementary Materials
www.sciencemag.org/cgi/content/full/science.1221920/DC1
Texts S1 to S8
Tables S1 to S8
Figs. S1 to S26
Movie S1
References (31–109)
14 March 2012; accepted 5 April 2012
Published online 12 April 2012;
10.1126/science.1221920
Mechanical Control of Morphogenesis
by Fat/Dachsous/Four-Jointed
Planar Cell Polarity Pathway
Floris Bosveld,
1
*Isabelle Bonnet,
1
*Boris Guirao,
1
*Sham Tlili,
1
†Zhimin Wang,
1
Ambre Petitalot,
1
Raphaël Marchand,
1
Pierre-Luc Bardet,
1
Philippe Marcq,
2
François Graner,
1
Yohanns Bellaïche
1
‡
During animal development, several planar cell polarity (PCP) pathways control tissue shape
by coordinating collective cell behavior. Here, we characterize by means of multiscale imaging
epithelium morphogenesis in the Drosophila dorsal thorax and show how the Fat/Dachsous/
Four-jointed PCP pathway controls morphogenesis. We found that the proto-cadherin Dachsous
is polarized within a domain of its tissue-wide expression gradient. Furthermore, Dachsous
polarizes the myosin Dachs, which in turn promotes anisotropy of junction tension. By combining
physical modeling with quantitative image analyses, we determined that this tension anisotropy
defines the pattern of local tissue contraction that contributes to shaping the epithelium mainly
via oriented cell rearrangements. Our results establish how tissue planar polarization coordinates
the local changes of cell mechanical properties to control tissue morphogenesis.
Tissue morphogenesis requires the coordi-
nation of cell behaviors during develop-
ment. Planar cell polarity (PCP) pathways,
which coordinate the polarization of cells in the
tissue plane, have been shown to play a funda-
mental role in morphogenesis of vertebrates and
invertebrates (1). It remains largely unknown
how PCP pathways control local cell mechan-
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ical properties to drive global tissue deforma-
tion. The Fat/Dachsous(Ds)/Four-jointed(Fj) PCP
pathway plays fundamental roles in the regulation
of tissue growth, the orientation of cell polarity
across the tissue, and the regulation of morpho-
genesis (1,2). fat and ds encode proto-cadherins,
whereas fj encodes a Golgi kinase modulating
Fat/Ds binding (3–8). In many Drosophila tissues,
ds and fj are expressed in tissue-wide oppos-
ing gradients (4,5,9,10). Fat and Ds are re-
ported to be homogeneous at the cell membrane
(10,11). Yet, the heterophilic binding of Fat and
Ds between adjacent cells is proposed to generate
a tissue-wide polarity (7,8,10,12–15). Through
a poorly understood mechanism involving Fat
signaling and the DHHC palmitoyltransferase
Approximated (16), this polarity promotes the
asymmetric distribution of the myosin Dachs,
which controls division orientation and apical
cell size (12,16–19). The role of the Fat/Ds/Fj
pathway in tissue morphogenesis has been studied
by using indirect measurements such as the shape
of clones and division orientation (19,20); con-
versely, measurements of tissue dynamics have
so far characterized its role in tissue rotation (21).
Here, we assessed whether, where, and how the
Fat/Ds/Fj pathway affects local cell mechanical
properties to drive tissue deformations.
We implemented a multiscale imaging meth-
od to record morphogenesis of the Drosophila
dorsal thorax during metamorphosis (22). This
monolayered epithelium is composed of a pos-
terior region, the scutellum, and of a large ante-
rior region, the scutum (Fig. 1A and fig. S1, A
and B). Cells were labeled with E-Cadherin:
green fluorescent protein (GFP), and the tissue
was imaged from 11 hours after pupa formation
(hAPF) to 36 hAPF by acquiring high-resolution
three-dimensional stacks tiling the thorax at each
time-point (Fig. 1A and movie S1). This multi-
scale imaging enabled us to follow ~10
4
cells over
several cell cycles with unprecedented dynam-
ics: 5 min resolution over 26 hours of develop-
ment and 0.32 mm resolution over the ~750 ×
700 mm
2
of the tissue. At the cell-scale, the spa-
tial and temporal resolutions facilitated the de-
termination and the tracking of cell apex areas,
cell shapes, divisions, cell rearrangements, and
apoptoses (Fig. 1, B to D; fig. S1, C and D; and
movie S2). At the tissue scale, we measured lo-
cal tissue flow over the whole tissue by means
of image correlation, using a length scale of 10
to 20 cells and a time scale of 2 hours. This re-
vealed the different periods of development (fig.
S2 and movie S3). In particular, between 17:20
and 21:20 hAPF the velocity map showed mor-
phogenetic movements both in the scutum and
the scutellum (Fig. 1E, shaded regions). This tissue
flow promoted tissue contraction and elongation
in the lateral scutum and the medial scutellum,
resulting in their anterior-posterior and medial-
1
Polarity, Division and Morphogenesis Team, Institut Curie,
CNRS UMR 3215, INSERM U934, 26 Rue d’Ulm, 75248 Paris
Cedex 05, France.
2
Laboratoire Physico-Chimie Curie, Institut
Curie, CNRS UMR 168, Université Pierre et Marie Curie, 26
Rue d’Ulm, 75248 Paris Cedex 05, France.
*These authors contributed equally to this work.
†Present address: Matière et Systèmes Complexes, Université
Paris Diderot, CNRS UMR 7057, 10 Rue Alice Domon et Léonie
Duquet, 75205 Paris Cedex 13, France.
‡To whom correspondence should be addressed. E-mail:
yohanns.bellaiche@curie.fr
Fig. 1. The Drosophila dorsal thorax as a system for mor-
phogenesis. In all figures, yellow circles, macrochaetae; cyan
dashed line, midline. (A) Dorsal thorax tissue labeled with
E-Cad:GFP. Yellow region, scutellum; dashed black line, scu-
tum. The black box cut by the midline defines the two “hemi-
scutella”.(Bto D) Maps of proliferation (B), apex area (C),
and anisotropy (D), defined as 1 minus the ratio of minor and
major axes of the fitting ellipse. White cells are sensory or-
gan precursor cells. (E) Velocity field averaged between 19
and 21 hAPF, represented as arrows. Gray regions are scutum
and scutellum flows. (F) Deformation rates averaged between
19 and 21 hAPF, represented as ellipses. Red, elongation; Blue,
contraction. Anterior (A). Posterior (P). Scale bars, 100 mm, 9 ×
10
−2
mm/min [(E), blue arrow], 2.4 × 10
−3
min
−1
[(F), blue bar].
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lateral elongations, respectively (Fig. 1F, scutellum
in yellow). Collectively, our multiscale imag-
ing and measurements provide a resource to in-
vestigate how signaling pathways control tissue
morphogenesis.
Looking for regulators of these morphogenet-
ic movements, we observed that ds and fj were
both expressed in the scutellum (fig. S3), their
opposing gradients forming an inverted V-shaped
domain pointing toward the midline (thereafter
referred to as L−shape) in each hemi-scutellum
(Fig. 2A and fig. S3). To understand the role of
Fat/Ds/Fj signaling in tissue morphogenesis, we
thus focused on the contraction and elongation
taking place in the scutellum. The average tissue
deformation rate map between 17:20 and 21:20
hAPF revealed that tissue deformation was not
homogenous along the ds and fj gradients (Fig.
2B and fig. S4). This suggests that Fat/Ds/Fj
activation might vary along the ds and fj gra-
dients and emphasizes the need to define where
the Fat/Ds/Fj pathway is active to investigate
its role in morphogenesis. Given the evidence
indicating that the subcellular localization of
the myosin Dachs is controlled by Fat activity
(17,18,23), we generated a Dachs:GFP (D:GFP)
rescue construct and imaged it in the scutellum
(movie S4). This revealed that (i) D:GFP was polar-
ized in the L-shaped domain, where the opposing
expression gradients of ds and fj meet (Fig. 2C);
and (ii) within the regions of D:GFP planar po-
larization, cell boundaries enriched in D:GFP
were aligned with each other, leading to D:GFP
planar polarity lines (Fig. 2C, arrowheads).
Loss of ds or fat function as well as over-
expression of fj disrupted D:GFP polarization
(fig. S5, A to D). In agreement with the fact
that D:GFP was mostly polarized in the region
where the ds and fj gradients were opposed,
clonal overexpression of either ds or fj induced
repolarization of D:GFP only in regions where fj
or ds were expressed, respectively (fig. S5, E
and F). We then analyzed the subcellular lo-
calizationofFat,Ds,andFjinrelationwiththe
Dachs polarization domain (fig. S6, A to C’’ )
and established that Ds was polarized in regions
where D:GFP was polarized (Fig. 2D and fig.
S6, A to A’’). Ds polarization required the fj gra-
dient and Fat activity but was independent of
Dachs activity (fig. S6, D to G’). Both Ds and
D:GFP polarized toward high levels of fj expres-
sion and colocalized at the junctions (Fig. 3, A
to C’’). Furthermore, D:GFP can pull down the
Flag:Ds intracellular domain (Fig. 3D). Alto-
gether, our results revealed that Ds is planar
polarized in the region where the opposing gra-
dients of ds and fj meet. In turn, the interaction
between Ds and Dachs promotes the polariza-
tion of Dachs (fig. S7, model).
The ectopic accumulation of Dachs reduces
cell apex area, suggesting its possible implica-
tion in mechanical apex constriction (19). To
directly assess whether the Fat/Ds/Fj pathway
modulates cell mechanical properties via Dachs
polarization, we performed laser ablation of junc-
tons and observed that the tension of junctions
enriched in D:GFP was on average twofold
higher as compared with junctions devoid of D:
GFP (Fig. 3E, fig. S8, and movie S5). To con-
firm that Dachs polarization leads to anisotropic
junction tension, we generated fat clones that in-
duced an increased polarization and an accu-
mulation of Dachs in mutant junctions facing
the wild-type ones (fig. S9, A and C). Such junc-
tions displayed an increased tension that depends
on Dachs activity (fig. S9B). Last, MyosinII
was not polarized at the fat clone boundaries
and did not exhibit a stronger anisotropy than
the one due to cell shape itself, along the Dachs
polarity lines (fig. S9, D to H). This shows that
Dachs polarity regulates the anisotropy of junc-
tion tension and suggests that the opposing ds
and fj gradients generate a tension anisotropy
along Ds and Dachs polarity lines.
To investigate whether the tension anisotropy
along the Dachs polarity lines control tissue
morphogenesis, we developed a physical model
that provides a general method to analyze the
morphogenetic contribution of a specific signal-
ing pathway within elaborate morphogenetic
movements. In our case, it predicted that Dachs
tension anisotropy is sufficient to modulate the
local contraction rate (supplementary text). It
provided a quantitative test to determine whether
Dachs contributes to morphogenesis: Upon sub-
traction of the contraction rate of any mutant
condition abrogating Dachs function or polar-
ization from the contraction rate of the wild-type
condition, the resulting difference in contraction
rate is expected to be aligned with the Dachs po-
larity pattern.
To analyze the role of Dachs polarization,
we first quantified the Dachs polarity pattern
Fig. 2. Ds and Fj expression
gradients locally polarize
Dachs and Ds. Panels show
right-side hemi-scutellum.
(A) Quantification of the av-
erage gradients of Ds and
fj-lacZ (n= 7 hemi-scutella).
(B) Mean deformation rates
(n= 5 hemi-scutella) between
17:20 and 21:20 hAPF. De-
formation rates represented
as ellipses. Red, elongation;
Blue, contraction. (Cand D)
Dachs:GFP (D:GFP) and Ds lo-
calization. Arrowheads: D:GFP
(C) and Ds (D) polarity lines.
Yellow ellipses indicate aver-
age macrochaete positions T
SD.Scalebars,10mm, 10
−3
min
−1
[(B), blue bar].
Fig. 3. Ds and Dachs colocalize and Dachs polar-
ization is associated with tension anisotropy. (A
and B) Cells located in a region of the Fj gradient
expressing D:GFP and lacking D:GFP (D:GFP
–
)(A),
or overexpressing ds (ds
UP
cells marked by mRFP,
not shown) (B) accumulate D:GFP and Ds at junc-
tions facing the higher Fj concentration (green
arrowheads), whereas they are absent at junctions
facing the lower Fj concentration (red arrowheads).
Yellow arrows: direction of polarization. Yellow dots:
dsUP cells abutting the wild-type (WT) cells (B). (Cto
C”)D:GFP[(C)and(C’’)] and Ds [(C’)and(C’’)]
colocalize (arrowheads). (D) Anti-Flag blot of GFP-
immunoprecipates from cells expressing Flag:Ds
intra
and GFP; Flag:Ds
intra
;Flag:Ds
intra
and D:GFP; Mo-
lecular weight (MW) markers in kilodaltons. Al-
though a nonspecific GFP binding was observed, a
larger amount of Flag:Ds
intra
was reproducibly copre-
cipitated with D:GFP. (E)Plotofthemeanspeedof
vertex relaxation after ablation of junctions with high
or low D:GFP. Scale bars: 10 mm.
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(Fig. 4, A and B, green bars, and fig. S10). We
then knocked down Dachs or Ds function by
expressing dachs (dachs
RNAi
)ords (ds
RNAi
)hair-
pins during pupal development and averaged
between 17:20 and 21:20 hAPF the map of dif-
ferences of the local contraction rates between
wild-type and dachs
RNAi
or between wild-type and
ds
RNAi
pupae. We observed significant differences
in the local contraction rates between wild-type
and dachs
RNAi
tissues or between wild-type and
ds
RNAi
within the L-shaped domain of D:GFP
polarization (Fig. 4, C and D, blue bars, and fig.
S11, A to C). The orientations of the significant
differences were aligned with the local orienta-
tions of the D:GFP anisotropy distribution (Fig.
4, C’and D’). These results demonstrate that
Dachs polarization regulates tissue morphogen-
esis by increasing the rate of contraction along
its polarity lines.
We then studied how Dachs polarization
controls the cell dynamics that makes up the local
tissue contractions. Our analyses of cell division
rate and orientation argue against a major con-
tribution of division orientation (fig. S12). We
therefore quantified the respective contributions
of cell rearrangements and cell shape changes to
tissue contraction rates (fig. S13). In the wild-
type tissue, Dachs polarization correlates with the
cell rearrangement pattern both in magnitude and
orientation (fig. S14, A to C’, red bars), whereas
it poorly correlates with cell shape changes (fig.
S14, D and D’, cyan bars). Accordingly, both the
differences in tissue contraction rates between
wild-type and dachs
RNAi
and between wild-type
and ds
RNAi
were mainly associated with a decrease
in the contribution of cell rearrangements to tissue
contractions in the regions of Dachs polariza-
tion and, to a lesser extent, to cell shape changes
(P<10
−12
)(Fig.4,EtoF’, and figs. S11, A’to C”,
and fig. S15). Similar results for tissue contrac-
tion rate and cell dynamics were obtained in
fat
RNAi
and fj
UP
mutant conditions (fig. S16).
Accordingly, ds
RNAi
,fj
UP
,fat
RNAi
,anddachs
RNAi
pupae manifest similar defects in the adult scu-
tellum shape (fig. S17).
Altogether, we found that Ds polarization
promotes Dachs polarization within a domain
of the opposing tissue-wide ds and fj gradients.
Their local polarization produces an anisotropic
distribution of junction tensions, which increases
the contraction rates along the lines of Ds and
Dachs planar polarization to shape the epithelial
tissue mainly through oriented cell rearrange-
ments (fig. S18). The Dachs myosin has the nec-
essary domains to be an actin-binding motor
(fig. S9) and, in complex with Dachsous, may
directly contribute to junction contractility, fav-
oring cell rearrangements. Because MyosinII also
contributes to junction tension and cell rear-
rangements (24), future work should dissect the
respective roles of Dachs and MyosinII in these
processes. Morphogenesis is accomplished by the
concerted activity of multiple signaling pathways.
Our subtractive method of tissue deformation rates
is general enough to isolate the contribution of a
given pathway to morphogenesis without making
assumptions on its magnitude and its spatial de-
pendence. Last, given the multitude of cell shapes,
cell sizes, and division patterns occurring in the
thorax epithelium, future work on this tissue should
reveal how multiple signaling pathways are inte-
grated to regulate proliferation, planar polariza-
tion, and morphogenesis.
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Acknowledgments: We thank J. Axelrod, S. Blair, Y. Hong,
K.Irvine,E.Martin-Blanco,M.Simon,D.Strutt,S.Tsukita,the
Bloomington Drosophila Stock Center, Transgenic RNAi Project,
and Vienna Drosophila RNAi Center for reagents; M. Coppey,
A. Houdusse, F. Molino, S. Ritzenthaler, F. Serman, J. Shi,
and the PICT-IBiSA@BDD for help; V. Hakim, E. Heard,
J. Lopez-Gay, M. Labouesse, and A-M. Lennon for comments.
This work was supported by ARC-4830, L’Agence Nationale
de la Recherche–MorphoDro, and European Research
Council–CePoDro grants; a Fondation pour la Recherche
Médicale grant to I.B.; and a Nederlandse Organisatie voor
Wetenschappelijk Onderzoek–Rubicon grant to F.B.
Supplementary Materials
www.sciencemag.org/cgi/content/full/science.1221071/DC1
Materials and Methods
Supplementary Text
Figs. S1 to S20
References
Movies S1 to S5
27 February 2012; accepted 30 March 2012
Published online 12 April 2012;
10.1126/science.1221071
Fig. 4. Dachs polarity lines promote local contrac-
tions mainly via cell rearrangements. Averaged
maps between 17:20 and 21:20 hAPF. (Aand B)
Localization of D:GFP (A) and map of D:GFP mag-
nitude and anisotropy (B) quantified by Fourier
Transform (FT, n=3hemi-scutella).(Cto F’)
Maps of subtractions of dachs
RNAi
(n=5hemi-
scutella) from WT (n= 11 hemi-scutella) and of
ds
RNAi
(n= 5 hemi-scutella) from WT (n=11hemi-
scutella) for contraction rates [(C) and (D)] and for
cell rearrangements [(E) and (F)]. Bars indicate
amplitudes and orientations of the differences of
contraction rates or cell rearrangements. Maps of
the alignment coefficients between the D:GFP FT
pattern and the differences in contraction rates [(C’)
and (D’)], or between the differences in contraction
rates and cell rearrangements within the D:GFP FT
pattern [(E’)and(F’)] for WT and dachs
RNAi
[(C’)and
(E’)] and for WT and ds
RNAi
[(D’)and(F’)]. Local
alignment scores [(C’)and(D’), orange; (E’)and
(F’), purple] go from 0 (fully anticorrelated), to
1 (fully correlated), through 0.5 (noncorrelated).
Significant data are green (B), blue [(C) and (D)],
and red [(E) and (F)] bars; other are gray bars [(B)
to (F)]. The average score Ais calculated over
nongray regions. Scale bars, 10 mm, 5.5 × 10
−4
min
−1
[(C) and (D), blue bars], 1 mm
2
min
−1
[(E)
and (F), red bars].
www.sciencemag.org SCIENCE VOL 336 11 MAY 2012 727
REPORTS
on May 11, 2012www.sciencemag.orgDownloaded from

www.sciencemag.org/cgi/content/full/science.1221071/DC1
Supplementary Material for
Mechanical Control of Morphogenesis by Fat/Dachsous/Four-Jointed
Planar Cell Polarity Pathway.
Floris Bosveld, Isabelle Bonnet, Boris Guirao, Sham Tlili, Zhimin Wang, Ambre
Petitalot, Raphaël Marchand, Pierre-Luc Bardet, Philippe Marcq, François Graner,
Yohanns Bellaïche*
*To whom correspondence should be addressed. E-mail: yohanns.bellaiche@curie.fr
Published 12 April 2012 on Science Express
DOI: 10.1126/science.1221071
This PDF file includes:
Materials and Methods
Supplementary Text
Figs. S1 to S20
References
Other Supplementary Material for this manuscript includes the following:
(available at www.sciencemag.org/cgi/content/full/science.1221071/DC1)
Movies S1 to S5

Supporting Online Material (SOM)
Mechanical control of tissue morphogenesis
by the Fat/Dachsous/Four-jointed planar cell polarity pathway
Floris Bosveld1,∗, Isabelle Bonnet1,∗, Boris Guirao1,∗, Sham Tlili1,‡, Zhimin Wang1, Ambre Petitalot1,
Rapha¨
el Marchand1, Pierre-Luc Bardet1, Philippe Marcq2, Fran¸cois Graner1, Yohanns Bella¨
ıche1,
1Polarity Division and Morphogenesis team, Institut Curie, CNRS UMR 3215, INSERM U934,
26 rue d’Ulm, 75248 Paris Cedex 05, France.
2Laboratoire Physico-Chimie Curie, Institut Curie, CNRS UMR 168, Universit´e Pierre et Marie Curie,
26 rue d’Ulm, 75248 Paris Cedex 05, France.
∗These authors contributed equally to this work
‡Present address: Mati`ere et Syst`emes Complexes, Universit´e Paris Diderot, CNRS UMR 7057,
10 rue Alice Domon et L´eonie Duquet, 75205 Paris Cedex 13, France
Corresponding author: yohanns.bellaiche@curie.fr
Contents
1 Materials and methods 2
1.1 Flystocksandgenetics............................................. 2
1.2 Molecular biology ................................................ 2
1.3 Immunohistochemistry and fixed tissue imaging . . . ............................ 3
1.4 S2 cell culture and immunoprecipitation ................................... 4
1.5 Live imaging . ................................................. 4
1.6 Junctiontensionmeasurementbyablation.................................. 5
2 Quantitative data analysis 6
2.1 Quantification of tissue flow fields . . . ................................... 6
2.2 Comparing and averaging different movies .................................. 7
2.3 Quantification of D:GFP signal ........................................ 9
3 Theoretical model 10
3.1 Hypotheses ................................................... 11
3.2 Subtractivemethod .............................................. 11
3.3 Predictionsandexperimentaltests ...................................... 12
4 Segmented image analysis 13
4.1 Patterns of proliferation, cell apical area, and cell apical anisotropy ................... 13
4.2 Cell shape changes and rearrangements ................................... 14
5 Supporting figures and movies 15
5.1 Supporting figures ............................................... 15
5.2 Supporting movie captions . .......................................... 43
1

F. Bosveld et al. - Supporting Online Material
1 Materials and methods
1.1 Fly stocks and genetics
Fly stocks used in this study: UAS-ds (1), tub-FRT-GAL80-FRT-GAL4 UAS-mRFP (gift from E.
Martin-Blanco), UAS-fj[1062 ]UAS-fj[1762 ](2), ubi-E-Cad:GFP (3), E-Cad:GFP (4), fj[P1 ](5), dachs[GC13 ]
FRT40A (6), dachs[210 ]FRT40A (6), fat[1]FRT40A (6), fat[8]dachs[GC13]FRT40A (6), fat[G−rv]
FRT40A (7), sqh:mCherry (8); fly stocks from the Bloomington Stock Center: ds[05142 ], act5C-GAL4[25FO1 ],
tub-GAL4[LL7 ], tub-GAL80ts[10 ], tub-GAL80ts[2], UAS-fatRNAi[TRiP .JF03245 ], UAS-dsRNAi[TRiP .JF02842 ], ubi-
mRFP.nls FRT80B; fly stock from the VDRC Stock Center: UAS-dachsRNAi[v12555 ].Aubi-E-Cad:GFP
insertion on the third chromosome was made by mobilizing the ubi-DE-Cad:GFP present on the second
chromosome (3).
In all experiments the white pupa stage was set to 0 hour after pupa formation (hAPF), determined with
1 h precision. Mutant clones in the scutellum were generated using FLP/FRT mediated mitotic recom-
bination (9, 10). Clones were induced in second instar larvae by heat shock (20 min at 37◦C). Clonal
overexpression was achieved using a flip-out strategy (11) using the tub-FRT-GAL80-FRT-GAL4 transgene.
Overexpression studies were carried out using the GAL4/UAS system (12).
Temporal control of gene function was achieved by using the temperature sensitive GAL80ts (13). Embryos
and larvae were raised at 18◦C. Late third instar larvae were switched to 29◦C. After 24 to 30 h, pupae were
examined. Those which were timed as 11±1 hAPF were mounted for live imaging at 29◦C. Some others were
not mounted but kept further at 29◦C until a total of 48 h, transferred back to 18◦C, allowed to develop
until adult stage, then photographed to quantify the shape of adult scutella.
1.2 Molecular biology
To create a D:GFP transgene under the control of its endogenous promoter, we used recombineer-
ing (14, 15) to introduce a GFP tag at the C-terminus of the dachs CDS present in BAC clone
CH322-153C02 (BACPAC Resources Center). First a galK cassette, amplified with primers F (5’-CACAA
GGGGCAGAGCTTCCACGTTCCCTTCCAGTTCATGACGCTCAGTAAACCTGTTGACAATTAATCA
TCGGCA-3’) and R (5’-CAGATGGAATGAATGGAATCATAACCAGTTTGTTTCCACCAGTAGTCCTT
ATTCAGCACTGTCCTGCTCCTT-3’) (underscored letters for galK sequences), was inserted via recombi-
nation at the C-terminus of the dachs CDS. After positive selection the galK cassette was replaced with the
GFP tag, primers F (5’-CACAAGGGGCAGAGCTTCCACGTTCCCTTCCAGTTCATGACGCTCAGTA
AAATGGTGAGCAAGGGCGAGGA-3’) and R (5’-CAGATGGAATGAATGGAATCATAACCAGTTTGT
TTCCACCAGTAGTCCTTACTTGTACAGCTCGTCCATGC-3’) (underscored letters for GFP sequences)
via recombination and negative selection for galK. The resulting attB-P[acman-d:GFP]-CmR-BW was inte-
grated into the PBac{y[+]-attP-9A}VK00019 landing site at 68D2 creating d:GFP[VK19]. As a control the
untagged attB-P[acman-dachs]-CmR-BW was also integrated at this site, dachs[VK19 ]. Both d:GFP[VK19 ]
and dachs[VK19 ]rescue morphological defects and the viability of dachs[GC13 ]/dachs[210 ]animals.
The ubi-Baz:mCherry transgene was constructed from pUASp-Baz-GFP (16). First the GFP was removed by
2

F. Bosveld et al. - Supporting Online Material
digestion with NotI/XbaI and replaced with mCherry, amplified with primers F (5’-GACGGCGGCCGCAAT
GGTGAGCAAGGGCGAG-3’) and R (5’-CCGTCTAGATTACTTGTACAGCTCGTCC-3’), and digested
with NotI/XbaI, resulting in pUASp-Baz-mCherry. Next, a KpnI-XbaI fragment containing Baz:mCherry
was isolated from pUASp-Baz:mCherry and inserted, using identical restriction sites, between the ubiquitin
promoter and hsp27 terminator present in a modified pCasper4 (http://flybase.org). A ubi-H2B:RFP
transgene was constructed by removing an Acc65I-XbaI fragment from pUAST-H2B:RFP (17) contain-
ing H2B:RFP and inserting it using identical restriction sites between the ubiquitin promoter and hsp27
terminator present in a modified pCasper4. All transgeneses were performed by Bestgene.
1.3 Immunohistochemistry and fixed tissue imaging
For fixed tissue analyses, pupae were dissected at 18-20 hAPF as previously described (18). Primary an-
tibodies used were: rat anti-Fj (1:250) (19), rat anti-Ds (1:2000) (20), rabbit anti-Ds (1:500) (21), rab-
bit anti-β-galactosidase (1:2000) (Cappel Laboratories), rabbit anti-GFP (1:2000) (Molecular Probes), rat
anti-Fat (1:1000) (20), rat anti-DE-Cad (1:100) (DSHB, DCAD2). Secondary antibodies used were: Alexa-
488-conjugated goat-anti-rabbit IgG (Molecular Probes), Cy2-conjugated donkey-anti-mouse IgG (Jack-
son ImmunoResearch), Cy3-conjugated donkey-anti-mouse IgG (Jackson ImmunoResearch), Cy5-conjugated
donkey-anti-rat IgG (Jackson ImmunoResearch). Images were collected with a confocal microscope (LSM
710 NLO, Carl Zeiss). All images represent maximum projections of a Z-stack unless otherwise specified.
LacZ enhancer trap lines were used to reveal the gene expression domains of fj, fj[P1](5), and ds, ds[05142 ](22).
To quantify the opposing expression gradients of fj and ds, heterozygous fj [P1] (5) pupae (20 hAPF) were
fixed and labeled with antibodies against β-galactosidase to reveal the fj-lacZ enhancer trap expression
and antibodies against Ds to reveal the Ds protein gradient. Expression maps (1880 ×1770 pixels) were
averaged over 7 different pupae aligned according to the positions of the macrochaetae which were determined
by membrane staining with antibodies against E-Cadherin. Histograms of Fj and Ds images were equalized
and normalized between 0 and 1. Subtracting Ds from Fj resulted in an image in arbitrary unit in the range
[−1; 1]. A Gaussian lowpass filter of size 150 pixels with standard deviation 50 pixels was applied and the
resulting image represented as a filled contour plot where the Λ shape appears as the orange band, of value
∼−0.2 (Fig. 2A).
From 29 hAPF onwards, the anterior-posterior boundary between the scutellum and the scutum can be
easily distinguished since the scutellum and scutum are separated by rows of smaller cells. Therefore the
position of the boundary can be precisely positioned on time-lapse movies by tracking back this group of
smaller cells at earlier time-points. This reveals that the anterior-posterior boundary between the scutellum
and the scutum has an indented shape from 11 hAPF onwards; and that it is positioned between the group
of large and small cells located between the posterior dorso-central and the anterior scutellar macrochaetae.
On fixed tissue at 20 hAPF, the anterior-posterior boundary between the scutellum and the scutum can be
approximately positioned using these criteria.
3

F. Bosveld et al. - Supporting Online Material
1.4 S2 cell culture and immunoprecipitation
For cell culture experiments, a full length Dachs cDNA was Gateway cloned into pUbi-W-GFP (Drosophila
Genomics Resource Center) creating ubi-D:GFP. The Ds intra cellular domain (aa 3115 to 3557) was in-
serted by Gateway cloning in pActin-Flag-W (Drosophila Genomics Resource Center) resulting in pActin-
Flag:Dsintra.
Drosophila S2 cells were maintained at 25◦C in Schneider’s Drosophila Medium (Gibco), containing 10%
fœtal bovine serum inactivated at 65◦C, penicillin (50 mg/ml) and streptomycin (50 mg/ml) (Gibco).
1.8×107cells were transfected with expression vectors by the Effecten method (Qiagen), and 72 h post trans-
fection, cells were lysed at 4◦C in lyses buffer: 50 mM Tris-HCl (pH 8), 150 mM NaCl, 1 mM EDTA, 5 mM
glycophosphate, 0.1% Triton and protease inhibitor cocktail (Sigma). Total protein levels were determined
by the Bradford method (Bio-Rad). For immunoprecipitation, lysates were incubated with rabbit-anti-
eGFP antibodies coupled to protein A agarose beads. Cell lysates and immunoprecipitates were separated
by SDS-PAGE, transferred to PVDF membranes (Millipore) and probed with mouse anti-Flag primary
antibodies (Sigma) and subsequently with HRP-conjugated anti-mouse secondary antibodies (Jackson Im-
munoResearch). Western blots were revealed by an enhanced chemiluminescence (ECL) detection system
according to the manufacturer’s instructions (Amersham Biosciences).
1.5 Live imaging
1.5.1 Microscopy
Pupae were prepared for live imaging as described in (23). Typically pupae were imaged for a period of
15-26 h, starting at 11-12 hAPF, with an inverted confocal spinning disk microscope (Nikon) equipped
with a CoolSNAP HQ2 camera (Photometrics) and temperature control chamber, using Metamorph 7.5.6.0
(Molecular Devices) with autofocus.
Single position movies in the scutellum were acquired at either 25±1◦Cor29±1◦C, with a 5 min temporal
resolution (16-28 slices Z-stack, 0.5 μm/slice for ubi-E-Cad:GFP, E-Cad:GFP and 20-50 slices Z-stack,
0.3 μm/slice for D:GFP, ubi-Baz:mCherry). Acquiring 24 positions every 5 minutes (Z-stacks, 30 slices,
0.5 μm/slice) yielded a tiling of the whole dorsal thorax (311 frames).
1.5.2 Image treatment
Movies of ubi-E-Cad:GFP and E-Cad:GFP are maximum projections of Z-stacks, D:GFP and Sqh:mCherry
are average projections. They were obtained using a custom ImageJ routine (publicly available as the“Smart
Projector” plugin) and have been used for tissue flow analysis. Multiple position movies were stitched using a
customized version of the“StackInserter” ImageJ plugin. Image dynamics is defined as the decimal logarithm
of the ratio of the largest to smallest scale, expressed in “decades” or “orders of magnitudes”. Here, with 5
min temporal resolution over 26 h of development and 0.32 μm spatial resolution over the 750×700 μm2of
the tissue, we follow the ∼104cells with a dynamics of ∼3 decades in both space and time.
Movies of D:GFP and ubi-Baz:mCherry are average projections of Z-stacks. They were obtained using a
4

F. Bosveld et al. - Supporting Online Material
custom Matlab routine that automatically detects the local Zlevel showing the higher apical Baz:mCherry
signal and removes the underlying background signal, then projects slices around this Zlevel.
During the process of projection we kept records of slices containing the adherens junctions (i.e. the
maximum intensity positions along the Zaxis. We thus established topographical maps Z(X, Y ) across the
plane. The angle with the horizontal plane, θtilt, is at most 0.01 radian over the scutellum, and reaches 0.02
radian only in the most lateral parts of the scutum. In the results presented here, the absolute correction
due to this angle is thus negligible, (1 −cos θtilt )∼10−4, and the curvature correction due to the spatial
derivative of θtilt is negligible too.
1.6 Junction tension measurement by ablation
1.6.1 Laser ablation of individual cell junctions
Baz:mCherry and D:GFP scutellum tissues were imaged using a two-photon laser-scanning microscope (LSM
710 NLO, Carl Zeiss) in single-photon mode at a resolution of 100×100 pixels (pixel size = 0.18 μm) with
a bidirectional scan lasting δt = 156 ms. We used the 488 nm laser for D:GFP and the 561 nm one for
Baz:mCherry. “Low” and “high” D:GFP cell junctions were individually ablated using a Ti:Sapphire laser
(Mai Tai DeepSee, Spectra Physics) at 890 nm with <100 fs pulses with a 80 MHz repetition rate. The
laser power (typically ∼0.2 W at the back focal plane) was chosen to ablate a cell junction without creating
cavitation (24).
Ablations at junctions between wt and fat[G−rv]cells, and control ablations between differently marked wt
cells, were performed in pupae expressing both Baz:mCherry and D:GFP. Ablations of junctions between
wt and fat[8]dachs[GC13 ]cells were performed in pupae expressing only Baz:mCherry. All ablations were
performed in the scutum to avoid the endogenous polarization of Dachs.
1.6.2 Quantification of junction tension
Junction tension prior to ablation and relaxation speed of ablated junction vertices immediately after ablation
are considered to be proportional (25–28). Baz:mCherry images were first denoised using Safir software (29)
to improve the vertex localization accuracy. To determine the initial relaxation speed, the vertex-vertex
distance dvv of the pre-cut and post-cut ablated junction was measured manually (in blind procedure) using
ImageJ at n= 2 and n= 10 frames after ablation.
Since the relaxation deviates from linearity already in the first 10 time steps, the measured relaxation
speeds V2=dvv (2δt)−dvv(0)
2δt and V10 =dvv(10δt)−dvv (0)
10δt are not equal. However, they are roughly proportional
to each other, so that the conclusions obtained in Fig. 3E are robust with respect to the choice of n. Their
amplitude does not correlate with the direction of the ablated junction prior to ablation (fig. S8). Conversely,
as expected, the direction of the tension, and thus of the relaxation speed, fully correlates with the direction
of the junction prior to ablation.
Statistical tests for data significance were performed using the Matlab’s built-in function ttest2.m (two-
sample t-test).
5

F. Bosveld et al. - Supporting Online Material
2 Quantitative data analysis
In our mechanical description, the local velocity describes the movements in the scutum and the scutellum.
It includes all contributions to tissue morphogenesis regardless of their cellular origin, such as cell shape
changes, rearrangements, divisions, apoptoses.
As described in fig. S19 or in ref. (30), a translation and a rotation (represented as an arrow and a circle,
respectively) are movements which preserve the relative positions of cells. Change of size and/or shape thus
results from velocity of tissue parts relative to each other: this is measured by the space variation of the
velocity, i.e. velocity gradient, also called “deformation rate”, and represented as an ellipse. Removing the
size change from the deformation rate characterizes specifically the morphogenesis, i.e. change of shape:
this is measured by the “contraction rate”, and represented as a blue bar. We now develop these points one
by one; for more details, refer to textbooks (31, 32).
2.1 Quantification of tissue flow fields
2.1.1 Velocimetry
The local tissue flow within scutum and scutellum tissues was quantified using movies of pupae expressing
E-Cad:GFP or Baz:mCherry. For each movie, the flow field was obtained by image cross-correlation (IC)
velocimetry along sequential images using customized Matlab routines based on the particle image velocime-
try (33) toolbox, matpiv (http://folk.uio.no/jks/matpiv). Each image correlation window (hereafter
“IC-box”) was a 64×64 pixels square (∼20×20 μm2, pixel size 0.32 μm), had a 50% overlap with each
of its neighbors, and typically contained a few tens of cells: this size corresponded to an optimum in the
signal-to-noise ratio.
In each IC-box (i, j), the velocity field V(i, j, t) was measured by correlating two successive images, at times
tand t+Δtseparated by Δt= 5 min, and by performing a sliding average over 24Δt= 2 h to improve
the signal to noise ratio without loss of information. The velocity field Vwas represented with arrows,
expressed in μm.min−1. The tissue flow was identical when measured with E-Cad:GFP or Baz:mCherry.
Within any single pupa where both hemi-scutella were imaged, the flow field appeared precisely symmetrical
with respect to the midline: this acted as a control of the reliability of velocity measurements.
2.1.2 Tissue flow representations
Differentiating the velocity field yields the velocity gradient matrix, ∇V:
∇V=∂Vx
∂x
∂Vy
∂x
∂Vx
∂y
∂Vy
∂y .(1)
It is expressed in min−1; note that 10−3min−1=1/(1000 min) corresponds to a relative change of 1% in
10 min.
To represent it, three quantities derived from it, also expressed in min−1, were computed and represented,
as explained in fig. S19: the local deformation rate, contraction-elongation rate, and rotation rate. Mathe-
matically, these quantities are defined as follows:
6

F. Bosveld et al. - Supporting Online Material
•The deformation rate,∇Vsym. It is the symmetrized part of the velocity gradient:
∇Vsym =⎛
⎝
∂Vx
∂x
1
2∂Vx
∂y +∂Vy
∂x 
1
2∂Vx
∂y +∂Vy
∂x ∂Vy
∂y ⎞
⎠=∇Vsym
xx ∇Vsym
yx
∇Vsym
xy ∇Vsym
yy .(2)
Since ∇Vsym is a 2D symmetric matrix, it can be diagonalized and represented as an ellipse (fig. S19).
which axis lengths are proportional to the two eigenvalues. A positive eigenvalue corresponds to a direction
of elongation represented in red. Conversely, a negative eigenvalue corresponds to a direction of contraction
represented in blue. Four possible cases are thus represented by four types of ellipses. (i) A positive isotropic
dilation corresponds to two equal red bars. (ii) An ellipse with a red bar and a smaller blue bar is a traceless
contraction-elongation plus a positive isotropic dilation. (iii) An ellipse with a red bar and a larger blue
bar is a traceless contraction-elongation plus a negative isotropic dilation. (iv) A negative isotropic dilation
corresponds to two equal blue bars.
•The contraction-elongation rate,∇Vdev. It is obtained from the decomposition of ∇Vsym into two con-
tributions: its trace Tr ∇Vsym, which reflects the overall isotropic dilation rate of apical area; and the
traceless remaining part, also called the “deviator”, ∇Vdev:
∇Vsym =1
2Tr ∇VsymI+∇Vdev ,(3)
where I=10
01
is the identity matrix. Since ∇Vdev is symmetric and traceless, it can be diagonalized
with its two opposed eigenvalues ±λ, which represent the rate of contraction in one direction and an equal
rate of elongation in the perpendicular direction (and thus an effective change in tissue shape), at fixed
apical area. Such traceless contraction-elongation corresponds to two orthogonal bars of equal lengths, one
blue, one red. Since they are redundant, for clarity in all figures we plot only one: we choose the blue bar of
length |λ|in the direction of contraction (fig. S19).
•The rotation rate,ω. It is the anti-symmetric part of ∇V:
ω=1
2∂Vy
∂x −∂Vx
∂y .(4)
This is a real number; it is represented as a circle, which diameter is the rotation rate |ω|, and which color
reflects its sign: red is for clockwise rotation and blue is for counter-clockwise (fig. S19).
2.2 Comparing and averaging different movies
We aimed at averaging different hemi-scutellum movies corresponding to the same genotype, or comparing
movies corresponding to different genotypes. For that purpose, their common space and time coordinates
were defined as follows.
2.2.1 Space registration
Each hemi-scutellum movie was oriented with the midline along the top horizontal side. Spatial landmarks
(fig. S4A) were the positions of the two scutellar macrochaetae at 16:30 hAPF, when the sensory organ
7

F. Bosveld et al. - Supporting Online Material
precursor (SOP) cells divide (34), and the results were independent of the choice of this reference time. The
posterior scutellar macrochaeta defines the Xaxis and the lateral scutellar macrochaeta sets the Yaxis.
We find that the positions of macrochaetae are reproducible up to 15 μm. The intersection of these Xand
Yaxes defines the origin of the IC-grid, whereby (0,0) is centered around one IC-box (green dashed square
in fig. S4A). Each IC-box is then labelled by two integer numbers (i, j) which define our two-dimensional
space coordinates on a fixed square lattice (Eulerian representation). Averaging over space is implemented
by averaging over (i, j).
2.2.2 Time registration
While the hAPF was determined with 1 h absolute precision, the tissue rotation rate analysis provided a
better relative precision that we used to synchronize the different movies, as follows. In the region of the
tissue located near the origin of axes, we observed that the rotation rate (Eq. 4) systematically passed
through a maximum during the development: this rotation peak could be used as a biological reference
time. For that purpose, the rotation rate was measured and spatially integrated over a rectangular reference
window (IC-boxes labelled i=−2to6andj=−2 to 2). Plotting this average, ¯ωref window, versus frame
number yielded a bell-shaped curve (fig. S4B).
We applied a time translation to each movie so that these curves overlapped. We matched the portion
of the curve which had the steepest slope (fig. S4B’): we thus used the time corresponding to 3/4ofthe
peak value, in the ascent (rather than the maximum itself, which by definition had a vanishing slope).
Its value, averaged over n= 11 wt tissue movies was 18:40 hAPF. Hereafter, “hAPF” indicates the time
after this temporal translation has been applied. For instance, after synchronization, the maximum of the
contraction-elongation and rotation rates were consistently found at 19:20 and 19:40 hAPF, respectively.
This determination reached a ±1 interframe (i.e. ±5 min) relative precision in wt.
For experiments performed at 29◦C, the development is accelerated. This was taken into account by dividing
time intervals by 0.9 (as determined with ±0.05 precision by the widening of the wt rotation peak). Mutant
tissues were synchronized with the same procedure as the wt tissue, up to a 10 min precision (fig. S20).
2.2.3 Ensemble average
These spatial and temporal adjustments allowed us to assign a system of space-time coordinates (i, j, t)
common to any set of Nhemi-scutellum movies, from pupae with a given genotype g(wt or mutant). We
defined the ensemble averaged deformation rate:
∇Vsym
g(i, j, t)= 1
N
N

n=1 ∇Vsym
g(i, j, t, n).(5)
as well as its standard deviation δg∇Vsym. Averages and standard deviations were measured over the
space-time points (i, j, t) for which experimental data were available in all movies after synchronization
(intersection of the data). Since δg∇Vsym reflects our detection level, ∇Vsym
g(i, j, t) was considered as
significant if |λ|(i, j, t) was larger than δg∇Vsym(t) and plotted as blue bars, else as gray bars (Fig. 4C,D
and figs. S11A-C, S15A,B, S16C,D).
8

F. Bosveld et al. - Supporting Online Material
2.3 Quantification of D:GFP signal
Anisotropy of Dachs is due to a combination of cell shape anisotropy and of Dachs distribution around
each given cell (section 2.3.4), which both contribute to stress (section 3.2.2). To quantify and average
the Dachs signal distribution in wt hemi-scutella, we used movies of flies expressing both Baz:mCherry to
label cell adherens junctions, and D:GFP. The tissue flow analysis was performed on Baz:mCherry in order
to determine for all movies the spatio-temporal coordinates (i, j, t): these coordinates were then used for
D:GFP signal quantification.
2.3.1 Anisotropy of D:GFP
The 2D Fourier transform (FT) is a classical tool to extract the orientations of geometric patterns in an
image (35). For example, the FT of an image of a regular pattern (such as a sinusoidal grid, see fig. S10A)
leads to a FT whose signal is mainly in the direction orthogonal to the grid (fig. S10B-C) and can be
represented as a green bar (fig. S10D). More generally, an image can be decomposed into a set of frequencies
which reflect the existence, the spacing and direction of geometric patterns.
To assess the anisotropy of D:GFP signal distribution in each IC-box (fig. S10E), its 2D discrete FT was
performed using Matlab’s built-in function fft2.m. In order to reduce spectral artifacts introduced by IC-
box edges (35), the raw image was multiplied by a square cosine before computing its FT. To make the
analysis robust with respect to possible translations of the D:GFP pattern within the IC-box, only the FT
norm (and not its phase) was kept, and the same sliding average over2hasinflowanalysiswasperformed
to improve the signal to noise ratio. We determined its ensemble average over several movies, F(i, j, t)as
well as the corresponding standard deviation δ[F](t).
For each given (i, j, t), the FT’s norm was a function of the Fourier reciprocal space coordinates, F(˜x, ˜y, t),
corresponding to a distribution of gray levels. It was maximal at the center, (˜x, ˜y)=(0,0) and decreased
faster in the direction of the D:GFP pattern anisotropy than in the orthogonal direction (fig. S10F). This
function was binarized by keeping only the pixels (˜x, ˜y)havinggraylevelsabovethe80
th percentile. Such
thresholding yielded a cluster of points displaying anisotropically distributed positions (˜x, ˜y) (fig. S10G).
Its variance matrix ˜x2˜y˜x
˜x˜y˜y2!was then computed. The traceless part of this matrix had two opposed
eigenvalues ±μ:here|μ|quantified the variance of D:GFP pattern anisotropy, so that |μ|quantified its
standard deviation. The eigenvector with a negative eigenvalue typically reflected the direction of the D:GFP
pattern anisotropy.
2.3.2 Amount of D:GFP
In a semi-quantitative approach we constructed a number to quantify the observation that more contrasted
parts of the image were the ones where D:GFP amount was larger. The local contrast C(i, j, t) was thus
defined as a relative intensity, as follows. We noted P5and P95 the average intensity of the pixels below
the 5th percentile and above the 95th percentile, respectively. For each IC-box at a given space-time point
9

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(i, j, t), we then constructed the number C(i, j, t):
C(i, j, t)=P95(i, j, t)−P5(i, j, t)
P95(i, j, t).(6)
C(i, j, t) was found to range from 0.5 for lowest D:GFP signal regions up to 2 for highest D:GFP signal
regions.
2.3.3 Representation of D:GFP polarization: Q matrix
To combine the quantifications of anisotropy and amount of D:GFP signal, a matrix Q(i, j, t) was built as
follows. Its eigenvectors were those defined in section 2.3.1: they were typically parallel and orthogonal to the
main anisotropy direction of the local D:GFP pattern. Its eigenvalues were defined as ±C(i, j, t)|μ|(i, j, t),
where |μ|quantified the standard deviation of the D:GFP pattern anisotropy, and the weight Cquantified
the amount of D:GFP (section 2.3.2). We ensemble averaged Qover n= 3 movies.
Agreen bar of length C(i, j, t)|μ|(i, j, t) was plotted in the direction of the negative eigenvalue of Q(fig.
S10H). The bar length and direction reflected the visible characteristics of the D:GFP pattern, which could
be averaged. More precisely, we considered Q(i, j, t) as significant if |μ|(i, j, t) was larger than δ[F](t).
2.3.4 Comparisons of D:GFP, Sqh:mCherry and E-Cad:GFP anisotropies
As already mentioned, anisotropy of Dachs is due to a combination of cell shape anisotropy and of Dachs
distribution around each given cell. To disentangle these effects, we measured the anisotropy |μ|(i, j, t)
of D:GFP, Sqh:mCherry and of E-Cad:GFP in n= 3 movies at 25◦C for each condition (fig. S9G,G’,H).
The procedure was the same as in section 2.3.1, with the 70th percentile instead of the 80th, to adapt to the
movies quality.
The Sqh:mCherry and E-Cad:GFP patterns are similar and reflect cell elongations (compare figs. S9G’ and
H). Almost everywhere, they are not significantly different from zero. They are just below or just above the
threshold only at the few places where cells are much more elongated.
3 Theoretical model
We sought to investigate whether there was a connection between: (i) the observed D:GFP polarization; (ii)
the Dachs-related contribution to mechanical stress; and (iii) the Dachs-related contribution to tissue flow.
For that purpose, we have developed a physical model of the relation between stress and flow. This analysis
led to the identification of relevant quantities: first, a matrix characterizing the contraction rate; second, a
semi-quantitative estimate of stress based on a matrix characterizing Dachs polarization. Furthermore, the
model predicted that these matrices were linked and were locally proportional to each other: this predictions
was experimentally tested.
In short, the prediction of our physical model is: if D:GFP imposed a stress pattern to the tissue then
for every mutant affecting Dachs polarization, we should observe that the difference in tissue contraction
between this mutant and the wt condition should correlate with the D:GFP polarization pattern. Combining
10

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physical modeling and subtractive approach thus extracts and evidences the contribution of a given individual
pathway within an elaborated morphogenetic movement. It thus links genetics and mechanics in the context
of tissue morphogenesis. We explicit the model in the context of the dachsRNAi mutant condition. Similar
conclusions can be reached using the dsRNAi,fatRNAi or fjUP mutant conditions which affect the pattern of
Dachs polarization.
3.1 Hypotheses
We treated the flow in two dimensions because: (i) the dorsal thorax epithelium is a quasi-2D monolayered
tissue with negligible curvature; (ii) the network of the adherens junction belts which we image, and which
enables long-range transmission of in-plane stresses within tissues (36), is only a few μm thick; and (iii) the
visible in-plane components of the tissue flow velocity likely dominate its possible out-of-plane components.
Developing tissues have been observed to display simultaneously liquid-like behaviours (flow at large scale),
and solid behaviours (elastic deformations of cells, irreversible plastic shape changes) (37–39). However,
under the effect of active cell shape fluctuations (37) the liquid behaviour dominates (37, 39, 40) at times
larger than the characteristic visco-elastic time, which is reported to be of order of minutes (37, 39, 41).
Here, morphogenetic movements had a time scale of the order of 2 hours (velocity gradients at most of a
few hundredths of min−1). We then safely assumed that the dominant contribution to mechanical stress σ
was viscous (37, 42) and wrote (43):
σ=−p+2ηcomp Tr ∇VsymI+2ηeff ∇Vdev .(7)
Here pis the pressure; ηcomp a compressibility dissipation, which includes several contributions; ηeff is the
usual hydrodynamic viscosity: the subscript “eff” recalls that it is an effective viscosity which not only
includes the contribution of cytoplasmic viscosity, but also active contributions from the cytoskeleton, or
from neighbor rearrangements (37). The deformation rate ∇Vsym and the contraction-elongation rate ∇Vdev
are defined in Eqs. (2,3); the traceless part of the stress σdev is defined as in Eq. 3:
σdev =σ−1
2Tr σI=2ηeff ∇Vdev .(8)
Eq. 8, which is independent from the trace, reflects the contraction-elongation part of the flow, involved in
changes of shape (i.e. morphogenetic movements), and of interest in what follows.
3.2 Subtractive method
3.2.1 Modeling
Since Eq. 8 is linear, one can use it to write the stress in presence of Dachs, that is, in the wt context, σdev
wt ,
minus the stress in absence of Dachs, σdev
dachsRNAi:
σdev
wt −σdev
dachsRNAi =2ηeff ∇Vdev
wt − ∇Vdev
dachsRNAi.(9)
The left and right hand sides of Eq. 9 reflect the specific contribution of Dachs to the stress and to the flow,
respectively. We introduce the compact notations:
σDachs =σdev
wt −σdev
dachsRNAi ,(10)
∇VDachs =∇Vdev
wt − ∇Vdev
dachsRNAi .(11)
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In order to avoid confusion between the left and right hand sides of Eqs. 10,11, and since we only consider
the traceless parts of matrices in what follows, we have dropped the dev superscript. Using these notations,
Eq. 9 reads:
σDachs =2ηeff ∇VDachs .(12)
3.2.2 Measurable quantities
Eq. 12 establishes a proportionality relation between two quantities which can be measured in experiments.
In the right hand side, ∇VDachs can be directly measured. In the left hand side, since Dachs-rich cell
junctions were under a larger tension and were apparently distributed anisotropically, one could expect that
Dachs had an anisotropic contribution to σDachs: it was stronger in the direction of strong Dachs intensity
than in the perpendicular direction. This contribution to stress could be estimated by measuring both the
length and tension of each cell-cell junction (44). Here the tension measurement required the quantitative
determination of: (i) D:GFP amount based on fluorescent intensity, and (ii) of the relation between D:GFP
quantity and tension. Both (i) and (ii) were beyond the scope of this study.
Instead, we used the matrix Qbuilt in section 2.3.3 as a semi-quantitative measurement of Dachs distribution,
combining both cell shape anisotropy and Dachs distribution around each given cell. In the case where Dachs
was absent or isotropically distributed, the FT signal was zero or isotropic, and Qwas zero by construction.
Thus σDachs and Qvanished simultaneously; in a linear approximation one could thus reasonably expect
that they were proportional to each other:
Q= cst ×σDachs .(13)
3.3 Predictions and experimental tests
3.3.1 Predictions regarding experiments
Combining Eqs. 12-13 immediately yields a testable relation between two operationally measurable quanti-
ties:
Q= cst × ∇VDachs .(14)
Eq. 14 is our main prediction. It states that the distribution of Dachs planar polarization, measured by
D:GFP FT, correlates with the local subtraction of dachsRNAi from wt contraction-elongation rates.
Eq. 14 can thus be tested by comparing the patterns of Qand ∇VDachs in the scutellum. If there was a
direct or indirect causal relation between Qand ∇VDachs, and if this relation was indeed local, then patterns
of both matrix fields should look similar.
3.3.2 Tests
As a first test, one could perform a direct visual comparison of data. Indeed, after averaging over the time
interval 17:20 - 21:20 hAPF where contraction-elongation was the largest, similar qualitative features were
observed in the zones where Qor ∇VDachs were significant. The position, size and shape of these zones were
similar in both patterns. Within these zones, the orientation of Qand ∇VDachs appeared similar (compare
Figs. 4B and C; see also Fig. 4D).
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To make this test more quantitative, we quantified the local alignment between the blue bars of the con-
traction rate and the green bars of D:GFP patterns. These bars made a relative angle noted α(i, j). Since
bars were not oriented, αwas defined modulo π, and the local alignment could be characterized by:
A(i, j) = cos2α(i, j ).(15)
The alignment coefficient A(i, j)of∇VDachs (or of any other matrix) with the FT pattern Qwas coded in
orange, from 0 for fully anti-correlated, to 1 for fully correlated, through 0.5 for non correlated (Fig. 4C’D’,
fig. S14C’D’, fig. S16C’D’), on IC-boxes where both ∇VDachs and Qwere significant. Averaging Eq. 15
over these IC-boxes yielded its spatial average, A(indicated on top right of panels such as Fig. 4C’):
A=
i,j
w(i, j) cos2α(i, j )

i,j
w(i, j).(16)
Here the weights w(i, j) include the norms of both matrix fields, w(i, j )=|∇VDachs(i, j)|×|Q(i, j)|, averaged
over 17:20 - 21:20 hAPF. In practice these weights have only a small effect on Avalues. Areflects the overall
alignment of Qand ∇VDachs. If the bars of ∇VDachs and Qremained always perfectly orthogonal or colinear,
then A= 0 or 1, respectively. In between, Avaried between 0 and 1. In the case where ∇VDachs and Qwere
not correlated, their relative angle αvaried randomly, and A≈0.5. By running simulations with random
angles, with same sample size as in our experiments, we estimated the standard deviation around the mean
value A=0.5tobeσ=1.7×10−2. We used this value to determine the significance of the difference ΔA
between two measured values of Aby calculating the p-value, p=1−erf(ΔA/σ√2) (45).
4 Segmented image analysis
To reinforce the multiscale description of morphogenetic movements, from cell level to tissue level, we
performed detailed cell-level analysis. Images were denoised with the Safir software (29). Cell contours were
determined and individual cells were identified using a standard watershed algorithm, followed by several
rounds of manual corrections. Around 2.8 million cells (8.4 million cell-cell junctions) were segmented. Both
by manual tests on small subsamples, and by automatic tracking of false cell appearances or disappearances,
we estimated the error rate to be below 10−4, which was sufficient for the analyses presented here.
4.1 Patterns of proliferation, cell apical area, and cell apical anisotropy
Four wt scutellum movies at 25◦C were segmented over 156 frames. An in-house automatic software (Matlab)
tracked segmented cells through all images. It yielded maps of cell centroid displacements (fig. S12C), cell
lineages and lists of divisions (fig. S12B,C and Movie S2C,C’), and lists of apoptoses (Movie S2C,C’).
We detected 1591 divisions with an error rate estimated below 1%. The wt movies were synchronized using
IC analysis (section 2.2.2) to obtain an ensemble averaged number of divisions plotted versus hAPF with
again a sliding average over 24 Δt= 2 h. A division angle Θ was defined as the angle between AP axis and
the line connecting the centroids of the daughter cells in their first image of appearance. Division angles
were scored for Θ in [0◦,180◦]. For clarity, scores were represented in polar histograms (“rose plots”) around
the full circle by displaying both Θ and Θ + 180◦(respectively dark blue and blue in fig. S12B).
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For whole thorax movies (Movie S1), each image contained in average around 104cells and parts of the
movies were segmented. Measurements performed on single images yielded maps of cell apical area and
anisotropy (Fig. 1C-D and fig. S1C,D). The cell division pattern reported in Fig. 1B was determined
manually by visual tracking of cell divisions through all images. Cells in the anteriormost part get out of
focus due to tissue flow and elongation, so that we cannot determine the total number of cell divisions that
they undergo (gray cells in Fig. 1B).
4.2 Cell shape changes and rearrangements
To quantify cell shape changes, Rauzi et al. (see the figs. 5a and S4 of ref. (26)) used a matrix called
“texture” as defined in Eq. 6 of ref. (46). It is based on the links connecting each cell center with the
centers of its neighbors: it expresses, in μm2, the variance of link length in each direction. Separately,
rearrangements were counted and quantified as integer numbers. Similarly, Aigouy et al. (47) used a former
version of the texture as defined in the Eq. 1 of ref. (48), which expressed the variance of the cell junctions
in each direction. More precisely, they call “cell elongation” (defined in Eq. S25 of ref. (47)) the traceless
part of the texture. Again, rearrangements were quantified separately, and as integer numbers (see Fig. 4
of ref. (47)). Note that in a rearrangement a cell junction vanishes and a new junction is created. It is
sometimes followed by the opposite rearrangement, where the new junction vanishes and the original one is
re-created. Since counting rearrangements as numbers does not take into account the directions of junctions,
a rearrangement plus its opposite are counted as 1 + 1 = 2 rearrangements, although their total effect does
not contribute to tissue morphogenesis. Conversely, Butler et al. (49) used their own method (defined in
ref. (30)). They computed the contribution of cell shape change to flow. They then subtracted the cell
shape change rate from the tissue shape change rate. They thus indirectly inferred the correct contribution
of rearrangements to morphogenesis as matrices, i.e. including their amplitude but also their direction.
Here, to characterize cell dynamics in term of cell shape changes and cell rearrangements, we applied to
tissue morphogenesis a formalism based on texture, validated on foam dynamics (46). Overall, 10 wt, 5
dachsRNAi,5dsRNAi,4fatRNAi and 2 fjUP moviesat29
◦C were segmented and analyzed in the interval
17:20 - 21:20 hAPF. For each IC-box, we listed the cells iwhich centroid was in this box at time t.The
total texture Mof these cells was defined as (Eq. 6 of ref. (46)):
M(t)=
i
1
2
j
wijmij .(17)
Here jlabels each neighbor of cell i, the vector 
ij =(Xij ,Y
ij) is the link between the centers of cells iand
j, the factor 1/2 avoids counting twice each link, the weight wij is 1 for all normal links and 1/2 for the few
links belonging to a 4-fold vertex, and mij is the tensorial (or outer) product of 
ij by itself:
mij =
ij ⊗
ij =X2
ij XijYij
XijYij Y2
ij (18)
The texture thus expresses the variance of link length in all directions. The cumulative variation of texture
over these 4 hours under consideration, ΔM=M(t+ 4h) −M(t), was calculated in each IC-box.
Cell shape changes in each IC-box were defined as the rate of texture variation, ΔM/4h, and expressed in
μm2min−1(Eq. C3 in appendix of ref. (46)). Cell shape changes were measured as matrices, in order
14

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to retain information regarding their direction and anisotropy, relevant to characterize contributions to
tissue shape change. In what follows we do not use their trace, related to changes in cell sizes. They were
represented as cyan bars along the direction of cell contractions (fig. S13A).
Cell rearrangements too were directly measured as matrices in the same formalism and expressed in the same
units, namely μm2min−1(Eq. 11 of ref. (46)). In each IC-box, at time t, we listed cells iwhich centroid
was in this box at two successive images t,t+δt and did not divide during δt. The total rearrangement rate
of these cells was measured as R(4h)/4h where R(4h) was the sum of rearrangements at each time interval
δt, defined as follows:
R(δt)=
i
1
2⎛
⎝−
j
wijmij +
jg
wijmij ⎞
⎠.(19)
Here the sums are taken on links jwhich are lost during δt, that is, cells which were neighbors of iat tbut
no longer at t+δt (yellow lines in Movie S2C,C’): they contribute negatively. Similarly, links jgwhich are
gained during δt, that is, cells which become neighbors of iat t+δt (red lines in Movie S2C,C’) contribute
positively. They were represented as red bars along the direction of gained center-center links, thus in the
direction of lost cell-cell junctions (fig. S13B). If two cells transiently lose their junction, then regain it,
their link disappears then re-appears, and the total contribution of such back-and-forth rearrangement to
the rearrangement matrix is close to zero, as it should be. When a four-fold vertex was detected during
a rearrangement, the corresponding links (shown in lighter colours in Movie S2C,C’) were counted with
a weight 1/2 so that the total contribution of the corresponding rearrangement was independent of the
detection of the four-fold vertex.
Using movie registration in time and space, measurements were averaged over several movies, thus providing
a good signal to noise ratio. This enabled us to use our subtractive method (section 3.2.1) to calculate the
local differences in cell rearrangements and cell shape changes in wt and mutant conditions that contribute
to the differences in local tissue contraction rates. This led to the determination of the specific Dachs
polarization contributions to cell rearrangements or to cell shape changes. In turn, these contributions
were correlated with the differences in tissue contraction rates over regions of strong D:GFP polarization.
The mutual alignment coefficient Aof cell shape changes and contraction rate, or rearrangement rate and
contraction rate, was plotted in the spirit of section 3.3.2, without weights, at places where the FT pattern
Qwas significant (purple in Fig. 4E’F’, fig. S15A”B”, fig. S16E’-H’).
5 Supporting figures and movies
5.1 Supporting figures
In all figures, the positions of the macrochaetae and of the midline are indicated by yellow circles and by
a cyan dashed line, respectively. Data on flow, FT and division are averaged over 64×64 pixels squares
(∼20×20 μm2) and 24 interframes (2 h). Such space and time intervals are large enough to yield a signal
to noise ratio suitable for the analyses presented here, and small enough to observe relevant details in
morphogenetic movements.
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 
     

     







 







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Figure S1. Metamorphosis of the Drosophila dorsal thorax. The visible symmetry of the patterns
with respect to the midline underlines that they are finely regulated at the scale of 10-20 cell clusters rather
than at the individual cell level. Using Gaussian filters of increasing sizes confirms that these patterns become
completely symmetric when blurred above 10-20 cell sizes.
(A)Drosophila adult dorsal thorax. The visible part of the adult scutellum is shaded in yellow and the
scutum is outlined by a white dashed line. (B) Dorsal view of the Drosophila pupa without pupal case, here
at 14 hAPF. The white box indicates the position of the thorax. (C-D) Cell-level measurements at 11, 20,
29 and 35 hAPF during morphogenesis of the pupa dorsal thorax. (C) Cell apex area, in color code scale
from blue (10 μm2) to red (60 μm2). (D) Cell shape anisotropy, defined as one minus the ratio between the
minor to major axes of the best fitting ellipse, from green (0.1) to brown (0.6). The scutellum is outlined
by a white dashed line, the scutum by a black one. Scale bars: 250 μm (A, B), 100 μm (C, D).
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 










  

Figure S2. Tissue dynamics in the pupa dorsal thorax during metamorphosis. These maps are
representative of the three main phases of dorsal thorax development. (i) From 14 to 17 hAPF, no major
morphogenetic movement is observed (A, B), yet epithelial cells of the dorsal thorax undergo a first round of
division (fig. S12B and Movies S1, S2). The tissue undergoes only small local rotation (C). (ii) From 17 to
21 hAPF, a symmetric lateral to medial flow is observed within the lateral domain of the dorsal thorax (A’),
corresponding to the contraction of the lateral domains of the dorsal thorax (B’) and its anterior-posterior
elongation (B’ and Movie S3). This flow is associated with cell apical constriction in the lateral domain of
the scutellum (compare the 11 h and 20 h panels of Fig. S1C). Concomitantly, a medial to lateral flow is
observed in the scutellum (A’), corresponding to the contraction-elongation of its medial domain (B’) and its
dorsal-ventral elongation (B’ and Movie S3). During this period, extensive rotation is observed in the dorsal
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F. Bosveld et al. - Supporting Online Material
thorax (C’). (iii) From 21 to 36 hAPF, a symmetric lateral to medial flow and a major posterior to anterior
flow are observed in the scutum (A”). These flow are associated with contraction-elongation deformation of
its lateral domains (B”) and its anterior-posterior elongation, as well as with the contraction of the pupa
neck region. During this period the scutellum mostly expands in all directions (B”). High tissue rotation
rates are observed in the lateral domain of dorsal thorax (C”).
(A-C”) Maps at 15 (A-C), 20 (A’-C’) and 25 (A”-C”) hAPF. (A-A”) local velocities represented as vec-
tors. (B-B”) Deformation rates represented as ellipses: a direction of elongation is represented in red and
contraction in blue. (C-C”) Rotation rate represented by circle diameters: clockwise is represented in red
and counter-clockwise. The scutellum is shaded in yellow and the scutum is outlined by a black dashed line.
Scale bars: 100 μm (black bars), 9×10−2μmmin
−1(arrows in A-A”), 2.4×10−3min−1(blue bars in B-B”),
8×10−5min−1(circles in C-C”).
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A
B
high
low
fj-lacZ
ds-lacZ
high
low
C
C’ Ds
fj-lacZ
Figure S3. Gradients of fj and ds expressions are opposed in the scutellum. Whereasdshadan
elaborate expression in the dorsal thorax, fj was mostly expressed in the medial domain of scutellum. Hence
fj and ds are expressed in opposing domains in the scutellum and in the most posterior part of the scutum.
Anti-βgal staining of (A)fj-lacZ and (B)ds-lacZ in the pupa dorsal thorax at 19 hAPF. The scutellum
is outlined by a white dashed line. (C,C’) Average patterns (n= 7 pupae) of fj-lacZ (C) and Ds (C’)
determined in the region marked in A by a white box. Scale bars: 100 μm (A,B), 10 μm (C,C’), .
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0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
x 10
-4
time before synchronization (in frame no.)
Rotation rate averaged over the reference window (min-1)
14 16 18 20 22 24 26
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
x 10
-4
hAPF after synchronization
14 16 18 20 22 24 26
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
x 10
-4
hAPF after synchronization
BB’B”
X axis
Y axis
(0,0) (i=6,j=2)
Reference window
64x64 pixels (1 IC box)
A
macrochaeta
Figure S4. Spatio-temporal registration of movies. In order to compare different hemi-scutellum
movies corresponding to the same genotype, and/or average their measurements to improve the signal to
noise ratio, their common space and time coordinates were defined in two steps: first, spatial registration
of the IC grid using the positions of the two scutellar macrochaetae (A); second, time registration using the
point with the steepest slope before the rotation rate peak (B-B”).
(A) Image of a wt hemi-scutellum at 16:30 hAPF showing the landmarks used for spatial adjustment
between movies. The Xand Yaxes were determined using the positions of the macrochaetae at 16:30 hAPF.
Red rectangle (IC-boxes labelled i=−2to6andj=−2 to 2): window over which the rotation rate was
measured and spatially integrated, called “reference window”. Two IC-boxes are shown as dashed squares
with their space coordinates (i, j) indicated. (B-B”) Synchronization: graphs showing the rotation rate of 11
wt movies at 29◦C calculated in the reference window defined in A: (B) before and (B’) after synchronization
using as a reference 3/4 of the rotation peak in the ascent (set to 18:40 hAPF). (B”) Graph showing the
average rotation rate ±SD of the same 11 wt movies after space and time registrations. Scale bar: 20 μm (A).
21

F. Bosveld et al. - Supporting Online Material
1 2
1
2
E
1 2
2
1
D:GFP mRFP
F
D:GFP
ds
RNAi
wt
AB
fj
UP
fat
RNAi
CD
fj
UP
ds
UP
D:GFP
D:GFPD:GFP
D:GFP D:GFP D:GFPD:GFP
D:GFP mRFP
22

F. Bosveld et al. - Supporting Online Material
Figure S5. Regulation of Dachs polarization D:GFP planar polarity lines (A) are lost when the Ds
gradient is eliminated (B), Fat activity is abolished (C) or the Fj gradient is flattened (D). Furthermore,
creation of ectopic Ds-Fj gradient boundaries by overexpression of either Ds (E) or Fj (F) polarizes D:GFP
towards the highest concentration of Fj.
(A-D) Localization of D:GFP in wt (A), dsRNAi (B), fatRNAi (C) and fjUP (D) scutella. (E) Localization
of D:GFP (green, gray in close-ups) in wt cells and in cells overexpressing ds (dsUP cells marked by mRFP
expression, red). Close-ups in regions 1 and 2 show that ds overexpression polarizes D:GFP in region 1
(yellow arrows), where fj is highly expressed, but not in region 2 (white arrows) where fj expression is low.
Yellow dots indicate dsUP cells abutting the wt cells. (F) Localization of D:GFP (green, gray in close-ups)
in wt cells and in cells overexpressing fj (fjUP cells marked by mRFP expression, red). Close-ups in regions 1
and 2 show that fj overexpression polarizes D:GFP in region 2 (yellow arrows), where ds is highly expressed,
but not in region 1 (white arrows) where ds expression is low. Yellow dots indicate fjUP cells abutting the
wt cells. Scale bars: 20 μm (A-F), 10 μm (close-ups of E,F).
23

F. Bosveld et al. - Supporting Online Material
B”BB’
C”CC’
A”AA’
Ds
Ft
Fj
D:GFP
D:GFP
D:GFP
D:GFP Ds
D:GFP Ft
D:GFP Fj
dachs
210/GC13
wt fj
UP
dachs
210/GC13
fat
G-rv/1
D’ E’ F’ G’
DEF G
Ds Ds
Ds Ds Ds
Ds
Ds
Ds
24

F. Bosveld et al. - Supporting Online Material
Figure S6. Ds planar polarization is independent of Dachs activity, but requires Fat activity
as well as the graded distribution of Fj. Fat is enriched in some regions of the scutellum but is not
as clearly polarized as Ds (compare A-A” and B-B”). Fj is mostly localized in domains corresponding to the
ones detected by fj-lacZ reporter (Fig. 2A and fig. S3C). Fj accumulates in small intracellular punctuated
structures as expected for a Golgi resident protein. Ds is normally polarized in dachs210 /GC13 tissue. In
fatG−rv/1and fjUP pupae, Ds remains at the cell membrane, but Ds polarization is hardly detectable.
(A-A”) Localization of D:GFP (white in A, green in A”) and Ds (white in A’, red in A”) in the scutellum.
(B-B”) Same for Fat. (C-C”) Same for Fj. (D-G’) Localization of Ds in wt (D,D’), dachs210 /GC13 (E,E’)
and fatG−rv/1(F,F’) scutella, and in Fj overexpressing fjUP (G,G’) scutellum. D’-G’ are close-ups of the
regions outlined in D-G, respectively. Scale bars: 20 μm (A-G), 10 μm (D’-G’).
25

F. Bosveld et al. - Supporting Online Material









 

Figure S7. Regulation of Dachs asymmetric membrane localisation. Schematic: thin line, cell
membrane; thick line, nucleus. Genetic evidences show that Fat activity inhibits Dachs membrane lo-
calisation (6, 50), whereas the DHHC Palmitoyltransferase Approximated (App) enzyme promotes Dachs
membrane localisation (51). Fat and App are homogeneously distributed at the cell membrane (21, 51, 52).
Our results showing that Ds is asymmetrically distributed and that Ds can interact with Dachs permit to
propose that upon localisation of Dachs at the membrane by App, Ds polarizes Dachs distribution by two
complementary mechanisms: (i) in an autonomous manner, Ds promotes Dachs asymmetric distribution by
interacting with Dachs; (ii) in a non-autonomous manner, Ds polarizes Fat signalling in the neighboring
cell, thereby excluding Dachs from the cell membrane facing the one where Ds is enriched. Fat processing
and phosphorylation (not depicted) might contribute to the polarization of Fat activity in response to Ds
binding (??).
26

F. Bosveld et al. - Supporting Online Material
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Figure S8. Cell junction tension correlates with Dachs enrichment and not with junction
orientation. The D:GFP enriched junctions can be found at various orientations relative to the anterior-
posterior animal axis (Fig. 4A) and we have ablated an unbiased sample. We find that the amplitude of
relaxation speed, and thus the amplitude of the tension, does not correlate with the direction of the junction
prior to ablation: p-values determined using the circular-linear correlation defined in Eq 27.47 of (53) and in
(54) were larger than 0.05 (for high, low or all D:GFP levels they were p=0.32, 0.22 and 0.31, respectively).
We interpret this absence of correlation by stating that the junction tension depends on its level of Dachs,
while it does not depend on its orientation.
(A) Cell junctions with high or low D:GFP (arrows) 1560 ms prior to ablation. (A’) Images of
Bazooka:mCherry prior to and following ablation (see Movie S5). Arrowheads indicate the position of
vertices. (B) Plot of the initial relaxation speed (μms
−1) of vertices after ablation of cell junction with
high (red) or low (blue) D:GFP levels, versus direction of the junction prior to ablation, plotted in two
symmetrical hemicircles for clarity. Circles are V2and triangles are V10 (see section 1.6.2 for details). Scale
bars: 10 μm.
27

F. Bosveld et al. - Supporting Online Material

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  
Figure S9. Regulation of tension anisotropy by Dachs polarization independently of MyosinII
polarization. To assess whether Dachs regulates junction tension anisotropy independently of MyosinII
polarization we performed several experiments. First we measured cell junction tension at the border be-
tween mutant and wt cells using laser ablation in mosaic tissues. It is established that fat clones trigger
Dachs polarization at the interface between wt and fat mutant cells (6, 50). The interface between wt and
mutant cells therefore provides an artificial boundary to analyse the role of Dachs polarization in junction
tension by comparing the tension between wt and fat junctions and wt and fat, dachs double mutant junctions
28

F. Bosveld et al. - Supporting Online Material
(A). Our ablation experiments revealed that indeed these ectopic cell junctions enriched in Dachs exhibited
Dachs-dependent increase in cell junction tension (B). Furthermore, the interface between wt and fat cells
does not show MyosinII polarization, as shown by Drosophila Myosin light chain (Spaghetti squash, Sqh)
localization (compare C and D). Finally, we have simultaneously recorded D:GFP and Sqh:mCherry during
scutellum morphogenesis (E,E’). The quantification of their anisotropy by FT demonstrated that D:GFP is
strongly and significantly polarized within the scutellum whereas Sqh:mCherry is not (G,G’). For comparison
we also performed identical analyses on E-Cad:GFP movies during scutellum morphogenesis and found a
nearly identical polarization pattern as we observed for the Sqh:mCherry (H). Both the Sqh:mCherry and
E-Cad:GFP patterns were just below or just above the threshold at few places where cells are much elon-
gated. Everywhere else, they are not significantly different from zero. Combined, these results demonstrate
that Dachs polarization results in anisotropic interfacial tension. The molecular mechanism of how Dachs
generates tension remains to be characterized. However, Dachs is most closely related to the well character-
ized MyosinV and MyosinI (55) which have been shown to produce movement on actin using in vitro assays
(56, 57). Furthermore, sequence analyses of Dachs demonstrated that all the necessary domains to be an
actin motor (actin bindings site, nucleotide binding domain), and hence to produce force, are present (A.
Houdusse, personal communication). Dachs mostly differs from MyosinV or I in the transducer domain,
which determines the processivity of the myosin motor. Based on the sequence comparison of Dachs with
MyosinV or MyosinI, which have been crystallized and biochemically characterized (58, 59), the most likely
scenario is that the interfacial tension is generated by the contractile force generated by the motor activity
of the Myosin Dachs in complex with proto-cadherin Dachsous.
(A) Representative images of cell junction ablation between wt and fat cells (upper panels) and between
wt and fat dachs cells (lower panels) prior to ablation and after ablation (top right corner of each panel
indicates the time relative to ablation). Mutant cells are marked by the absence of nls:GFP. Yellow dots
indicate mutant cells abutting wt cells. Arrows indicate the ablated junctions and arrowheads the position
of the vertices. Cell junctions between wt and fat cells have increased amounts of D:GFP (first panel and see
also C). Ablations at junctions between wt and fat cells and control ablations (between differently marked
wt cells) were performed in pupae expressing both D:GFP and Baz:mCherry, while ablations of junctions
between wt and fat dachs cells were performed in pupae that expressed only Baz:mCherry. All ablations
have been performed in the scutum to avoid the endogenous polarization of Dachs. (B) Graph of the mean
initial relaxation speeds of vertices in junctions between wt and wt cells (1.07±0.46 μms
−1,n= 27), wt
and fat mutant cells (1.50±0.78 μms
−1,n= 27) and wt and fat dachs double mutant cells (0.85±0.64
μms
−1,n= 27). (C,C’) D:GFP (grey in C and green in C’) in wt and fat cells. Mutant cells are marked by
the absence of H2B:RFP (red in C’). D:GFP is enriched at the interface between wt and fat cells. (D,D’)
Sqh:mCherry (grey in D and green in D’) in wt and fat cells. Mutant cells are marked by the absence of
nls:GFP (red in D’). No polarization of Sqh:mCherry can be detected at the interface between wt and fat
cells. (E,E’) Images of the scutellum at 19 hAPF of a pupa expressing D:GFP (E) and Sqh:mCherry (E’).
(F) E-Cad:GFP in the scutellum at 19 hAPF. (G,G’,H) FT analyses of E,E’,F averaged between 17:20
and 21:20 hAPF (n= 3 for each panel): maps of the D:GFP (G), Sqh:mCherry (G’) and E-Cad:GFP (H)
anisotropy. Significant data: green bars; other: gray bars. In all panels, yellow dots indicate mutant cells
abutting wt cells. Scale bars: 10 μm.
29

F. Bosveld et al. - Supporting Online Material
D:GFP D:GFP D:GFP FT D:GFP F
T
-0.4 -0.2 0 0.2 0.4
ds fj
D:GFP FT
ABCD
D:GFP D:GFP FT
EFGH
Windowing
FT
Inertia
Matrix
-  trace
90° rotated
Q
IJKL
Figure S10. Quantification of D:GFP pattern anisotropy. A green bar is plotted in the direction of
D:GFP pattern anisotropy, quantified by 2D discrete Fourier transform (FT) analysis used to build the Q
matrix (section 2.3.3). It correlates with the position and shape of the opposing fj and ds gradients pattern.
(A-D) FT and construction of Qon a basic example. (A) Periodic sinusoidal pattern tilted at 45◦.(B)
FT norm of image A represented in the Fourier space, after an appropriate windowing (multiplication by a
square cosine) that minimizes the edge effects. The origin of the Fourier space has been shifted so that it
is at the center of the panel in the Fourier space, rather than in a corner. (C) Inertia matrix of the pixels
in B that are above the 80th percentile, represented as a green ellipse and overlayed to B. (D) The matrix
obtained in C has its trace removed (half trace subtracted from each diagonal term), the square root of its
positive eigenvalue is represented after 90◦rotation and multiplication by the contrast of A (here equal to 1).
The resulting green bar represents Qwhich quantifies the anisotropy and orientation of the pattern visible in
A. (E-H) FT and construction of Qfor an actual Dachs signal. (E) Raw image extracted from a time-lapse
D:GFP movie, cropped in an IC-box.(F) Same as B, averaged over 2 h. (G) Same as C. (H) Same as D.
(I-L) Pattern of D:GFP polarization. (I) Snapshot of D:GFP pattern. (J) Map of the D:GFP magnitude
and anisotropy determined by Fourier Transform (FT) on the average of D:GFP time-lapse movies (n=3)
between 17:20 and 21:20 hAPF. Significant data: thick green bars; other: thin gray bars. (K) Overlay of (I)
and (J). (L) Overlay of (J) and fig. 2A. Box size: 64 ×64 pixels ∼20 ×20 μm2(A,D,E,H). Scale bars: 10
μm (I-L).
30

F. Bosveld et al. - Supporting Online Material



 
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Figure S11. Contraction rates, cell rearrangements and cell shape changes in wt, dachsRNAi
and dsRNAi hemi-scutella. Having observed similarities between the wt contraction rate map (A) and
the Dachs signal pattern (Fig. 4A), we looked for the specific contribution to flow of Dachs and Ds (other
mutations of the Fat/Ds/Fj pathway are presented in fig. S16). The flow in wt, dachsRNAi and dsRNAi
tissues was calculated according to the right hand side of Eq. (11). Using the flow presented here (B-C),
we subtracted the contraction rates of dachsRNAi from wt (A-B), and of dsRNAi from wt (A-C), according
to Eq. (11). This yielded the maps presented in Fig. 4C,D. We then used the method explained in section
4.2 to measure the contributions of cell rearrangements (A’-C’), and of cell shape changes (A”-C”) to tissue
contraction. They too are represented as bars, as explained in fig. S13.
(A-C”) Maps of local contraction rate ∇Vdev (A-C), traceless parts of rearrangement matrix (A’-C’) and
of cell shape change matrix (A”-C”) between 17:20 and 21:20 hAPF in wt(A-A”), dachsRNAi(B-B”), and
dsRNAi(C-C”) scutella. Significant values are shown as thick colored bars, others are shown as thin gray
bars. Yellow ellipses indicate the ensemble average ±SD positions of the macrochaetae. Scale bars: 10 μm
(black bars); 5.5×10−4min−1(blue bars in A-C); 1 μm2min−1(red bars in A’-C’, cyan bars in A”-C”).
31

F. Bosveld et al. - Supporting Online Material
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
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 
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
 



'
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"& &
 $"$ 
 $ 
Figure S12. Contraction-elongation of the scutellum medial region does not correlate with
cell divisions. To investigate the role of cell division orientation in scutellum morphogenesis, we have first
compared the magnitude of tissue deformation with the timing and the orientation of cell division (A, A’ and
B). Second, we have compared the trajectories of cells with their division timing (C). We found three phases:
phase 1, before 17:20 hAPF no deformation is observed; phase 2, between 17:20 and 21:20 hAPF the medial
domain undergoes a contraction-elongation movement, and most cells of the scutellum medial domain move
laterally without undergoing cell division; phase 3, after 21:20 hAPF the tissue expands in all directions (A’).
During these three phases cell divisions are aligned along the tissue medial-lateral axis. The comparison of
the cell division rate with the magnitude of tissue deformation reveals that: (i) cell division rate, maximal in
phase 1, does not correlate with the magnitude of tissue deformation, minimal in phase 1; (ii) the strongest
contraction-elongation deformation of the scutellum medial domain (phase 2) occurs between two waves of
32

F. Bosveld et al. - Supporting Online Material
cell divisions (phases 1 and 3); (iii) during each wave of cell divisions (phases 1 and 3), the orientation of
cell division does not correlate with that of tissue deformation rate. Together, these results argue against a
role of cell division orientation in the contraction-elongation deformation of the scutellum medial region.
(A,A’) Local deformation rate averaged over 5 wt hemi-scutellum movies at 25◦C between 13:20 and
26:40 hAPF, represented as ellipses: a direction of elongation is represented in red and contraction in
blue. (A) Local deformation rate averaged between 17:20 and 21:20 hAPF. The solid and dashed rect-
angular boxes outline the domains where the kymograph in A’ and the cell division orientation in B are
measured, respectively. (A’) Kymograph of the deformation rate in the medial domain of the scutellum
(solid box in A). Note that the data presented in panels A-A’ are extensions of the data presented in Fig.
2B. (B) Division rate: graph of the ensemble average number of cell divisions per frame and symmetrized
rose plots of their orientation during the three phases of development measured in the dashed box in A,
obtained by segmenting and tracking each individual cell between 13:20 and 26:40 hAPF. The number of
cell divisions per frame was time averaged over 24 frames and ensemble averaged over 4 wt hemi-scutellum
moviesat25
◦C (total cumulated over 4 movies: n= 1591 divisions, with an error rate estimated <1%
by visual inspection of each frame). (C) 50 min cell trajectories during contraction-elongation movements.
Following the segmentation of a single time-lapse movie of the scutellum between 11:00 and 27:40 hAPF,
cell lineages, timing of each division and cell trajectories were determined. Cell trajectories are color coded
according to the number of cell divisions that each cell has undergone: pink for cells having divided once;
blue for cells having divided twice; green (a few cells are visible between the macrochaetae) for the third
wave of division which begins just before 22 hAPF (Movie S2B). The rectangular box (reference window,
same as in fig. S4A) outlines the domain where cell division orientations are measured in (B). Scale bars:
10 μm (A); 10−3min−1(blue bars in A and A’); 20 μm (C).
33

F. Bosveld et al. - Supporting Online Material
cell shape
changes
cell
rearrangements
A
B
Figure S13. Representation of quantitative analysis of cell rearrangements and cell shape
changes. Between the initial (left) and final (right) images, a tissue domain is undergoing a contraction
(here along the horizontal axis) accompanied by an elongation in the perpendicular direction. Such tissue
domain shape change may arise from processes such as cell rearrangements or changes of individual cell
shapes. For simplicity, cells are here sketched as identical, and both processes are depicted separately, but
the same quantitative analysis was performed on our experimental movies of the developing Drosophila dorsal
thorax where both processes may contribute together to local tissue deformations.
(A) Cell shape changes, represented by a cyan bar quantifying the number, the magnitude and the direction
of cell contraction (here horizontal). Since in this example all cells conserve their neighbors (thin cyan
lines), cell rearrangements have no contribution (red dot). (B) Round of oriented cell rearrangements:
horizontal junctions shrink and disappear (corresponding cell-center links are indicated by dashed red
lines). New vertical junctions appear and elongate (corresponding cell-center links are indicated by thin
cyan lines). Cell rearrangements are represented by a red bar quantifying the number, the length and
direction of lost junctions / new links (here horizontal). Since in this example all cells end up with the
same shape as in their initial state, cell shape changes have no contribution (cyan dot).
34

F. Bosveld et al. - Supporting Online Material




!!


"
"
!  
 
Figure S14. Dachs polarization, as quantified by Fourier Transform (FT), strongly correlates
with cell rearrangements and poorly correlates with cell shape changes.
(A,B) D:GFP pattern: (A) snapshot, the same as Fig. 2A, Fig. 4A, fig. S5A and fig. S10I. (B) Averaged
map of FT, the same as Fig. 4B and fig. S10J. (C,C’) Maps of cell rearrangements in wt (C) and of their
alignment coefficients with the D:GFP FT (C’). (D,D’) Same for cell shape changes. Significant data: color
bars; other: gray bars (C,D). The local score of the alignment with D:GFP FT (C’,D’) is coded in orange
from 0 for fully anti-correlated, to 1 for fully correlated, through 0.5 for non correlated. The overall score A
is indicated. Gray squares indicate IC-boxes where data were not significant: they were not included in the
calculation of A. Scale bars: 10 μm (A-D’), 1 μm2min−1(red bar in C, cyan bar in D).
35

F. Bosveld et al. - Supporting Online Material
'(wt-dachs
RNAi
)'(wt-ds
RNAi
)
AA’
B B’
A=0.66
A”
A=0.53
B”
cell shape changes alignment coefficient
contraction rate
Figure S15. Maps of local cell shape changes and of their correlation with contraction rates
in dachsRNAi or dsRNAi mutant conditions.
(A-B) Specific contribution of dachsRNAi (A) and dsRNAi (B) to contraction rate, calculated according to
the right hand side of Eq. (11). Same panels as in Fig. 4C,D. (A’-B’) Specific contribution of dachsRNAi
(A’) and dsRNAi (B’) to cell shape changes: the cell shape change (explained in section 4.2) of dachsRNAi
or dsRNAi mutant condition is subtracted from that of wt one. (A”-B”) Maps of the alignment coefficient
between the specific contraction rate (A-B) and cell shape changes (A’-B’) in dachsRNAi (A”) and dsRNAi
(B”). Data are represented only where D:GFP has a significantly non-zero FT signal. The local score of
the mutual alignment is coded in purple from 0 for fully anti-correlated, to 1 for fully correlated, through
0.5 for non correlated. The overall score A is indicated: cell shape changes score 0.66 and 0.53, while
cell rearrangements score a significantly higher (p<10−16) correlation at 0.8 and 0.77, respectively (Fig.
4E’,F’). Gray squares indicate IC-boxes where FT data were not significant: they were not included in the
calculation of A. Scale bars: 10 μm, 5.5×10−4min−1(blue bars in A, B), 1 μm2min−1(cyanbarsinA’,
B’).
36

F. Bosveld et al. - Supporting Online Material

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









('
('




(
(

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Figure S16. Analysis of tissue contractions, cell rearrangements and cell shape changes in
fjUP and fatRNAi scutella. To facilitate the comparison with Dachs and Ds analyses, the legend is the
same as in the corresponding figures: (A-B”) fig. S11B-C”, (C-F’) Fig. 4C-F’, (G-H’) fig. S15A”-B”.
Note the similarity of Fat data with Dachs and Ds. This analysis of cell rearrangements and cell shape
changes in fjUP and fatRNAi scutella confirmed the results obtained for dachsRNAi and dsRNAi, namely that
Dachs controls tissue contraction mainly by promoting cell rearrangements along its polarization pattern.
Cell rearrangements score at 0.73 and 0.78 (E’,F’), indicating significantly higher (p<10−12) correlations
than cell shape changes which score at 0.61 and 0.6, respectively (G’,H’).
(A-H’) Maps for fjUPand fatRNAi. Color-coded maps represent alignment coefficients between the difference
in contraction rate and: the D:GFP FT (C’,D’: orange); cell rearrangements within the D:GFP FT pattern
(E’,F’: purple); and cell shape changes within the D:GFP FT pattern (G’,H’: purple). Overexpression of fj
partially abrogated D:GFP polarity mostly in the anterior part of the Λ-shaped domain and, accordingly,
significant differences in the convergence rate were observed mostly in the anterior part (D).
37

F. Bosveld et al. - Supporting Online Material

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
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
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






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***
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

Figure S17. The Fat/Ds/Fj/Dachs pathway modifies the scutellum shape. fatRNAi (D-D”),
dsRNAi (E-E”), fjUP (F-F”), and dachsRNAi (G-G”) mutants in which we temporally abrogated the gradient
of fj expression or abrogated the function of ds, fat or dachs using the GAL80ts (13) resulted in the elongation
of the adult scutellum along its medial-lateral axis and in a higher anisotropy (defined in A). fat, ds, fj and
dachs hypomorphic alleles also affect tissue anisotropy (B). Since these genes have a well-characterized
role in growth/proliferation of third instar imaginal discs, conditional expression of dachsRNAi hairpins or
overexpression constructs at the end of the larval life are in our view a better demonstration of the role of the
Fat/Ds/Fj pathway during pupal development. These medial-lateral elongations agree with the respective
differences in contraction rates: the medio-lateral contraction in wt is replaced in mutants with an antero-
posterior contraction (Fig. 4 and fig. S11).
(A-B) Definition (A) and measurement (B) of scutellum anisotropy for hypomorphic mutations of fat,ds,
fj and dachs.(C-G”) Adult scutella (shaded yellow domains in C-G’) and measurements (C”-G”) of their
anisotropy for wt (C-C”), fatRNAi (D-D”), dsRNAi (E-E”), fjUP (F-F”), and dachsRNAi (G-G”) adults that
were raised at 18◦C, used as controls (C-G), or that were transferred to 29◦C for a period of 48 h (C’-G’).
Change in temperature from 18◦Cto29
◦C did not affect the wt scutellum shape. pvalues were determined
by Student’s t-test. Scale bars: 250 μm.
38

F. Bosveld et al. - Supporting Online Material
midline
macrochaetae
ds gradient
fj gradient
Dachs/Ds polarization domain
cell rearrangements
tissue constriction
contraction
Dachs/Ds polarity vectors
Local regulation of cell mechanics & dynamics
Coordination of Ds & Dachs cell polarization
Global Ds/Fj expression patterns
Contribution to global tissue morphogenesis
Figure S18. Graphical summary. Scheme of a Drosophila hemi-scutellum during metamorphosis (an-
terior to the right). Positional landmarks are indicated: macrochaetae as yellow dots, and midline as a
magenta dashed line. The tissue domain that undergoes strong constriction is marked in gray. In the scutel-
lum, tissue-wide expression gradients of Ds (red) and Fj (green) exists. These opposing gradients define
regions in which Ds is planar polarized (blue) and the orientation of the polarization (towards high Fj, yel-
low arrows). In turn Ds polarization results in the polarization of the Dachs myosin. Their local polarization
produces an anisotropic distribution of cell junction tensions, which contribute to increasing the contraction
rates (blue lines) along the lines of Ds and Dachs planar polarization to shape the epithelial tissue mainly
by oriented cell rearrangements (red lines).
39

F. Bosveld et al. - Supporting Online Material
  





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
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
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
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


Figure S19. Local deformation rate, contraction-elongation rate, and rotation rate. The velocity
gradient is decomposed into its symmetric and its anti-symmetric parts (31, 32). The deformation rate,
related to the symmetric part of the velocity gradient, reflects changes in tissue size and shape. From it we
separate the size changes to extract the contraction-elongation rate, which directly reflects effective changes in
tissue shape. The local rotation rate or vorticity, related to the anti-symmetric part of the velocity gradient,
does not by itself contribute to tissue shape change. Accordingly, contraction-elongation and rotation are
two quantities that can vary independently. If the velocity gradient has no symmetric part, the tissue rotates
as a whole, and there is no tissue shape change. If the rotation rate is spatially heterogeneous, the velocity
gradient has non-zero symmetric and anti-symmetric parts: in that case there are simultaneously a shape
change and a rotation, but they are not related, and again the rotation is not directly involved in tissue shape
change. We thus purposedly exclude the rotation from our analysis of morphogenetic changes, and use it
only to synchronise the movies (section 2.2.2 and fig. S4). To avoid ambiguities we do not use the words
“shear rate” which in the literature indicate either a symmetrized (B’) or a non-symmetrized (E) velocity
gradient.
Schematic, not drawn to scale, of the notations and definitions used in the text. (A) A global translation of
a tissue domain does not contribute to its shape or size change. (B-B”) A positive isotropic dilation (B) has
two equal positive eigenvalues (in red). A “contraction-elongation”(B’) represents perpendicular contraction
40

F. Bosveld et al. - Supporting Online Material
and elongation with the same amplitude: it has two opposite eigenvalues (red for positive, blue for negative),
and can be represented indifferently by a red bar and a blue one within a circle, or only by the blue bar for
clarity. A negative isotropic dilation (B”) has two equal negative eigenvalues (in blue). Dilations contribute
to tissue size change, contraction-elongation to tissue shape change. (C-C’) Combining a dilation and a
contraction-elongation results in a deformation rate with a larger positive eigenvalue (C=B+B’) or a larger
negative eigenvalue (C’=B’+B”). Since B’, C and C’ correspond to the same contraction-elongation, they
are represented by the same blue bar. (D) A rotation is represented by a circle, here red for clockwise (else,
blue for counter-clockwise). It does not by itself contribute to tissue shape or size change. (E) “Pure shear”
or “simple shear” can be decomposed in a contraction-elongation, which changes the shape, and rotation,
which changes the orientation (E=B’+D). The contraction-elongation is represented by a blue bar in the
direction of contraction. For details see section 2.1.2.
41

F. Bosveld et al. - Supporting Online Material
16 18 20 22
-4
-3
-2
-1
0
1
2
hAPF after synchronization
x 10-4
dachsRNAi
wt
dsRNAi
fjUP
fatRNAi
Rotation rate averaged over the reference window (min -1
)
Figure S20. Rotation rate in wt and mutant scutella during morphogenesis. Qualitatively the
peak of rotation rate in mutant scutella is the same as in wt, but quantitatively its amplitude is reduced.
Mean value (thick line) ±ensemble standard deviation (shade) versus hAPF after synchronization. The
rotation rate was space averaged over the reference window (fig. S4) and ensemble averaged over nmovies
of the same genotype. Blue, wt, n= 11 (same data as fig. S4B”); red, dachsRNAi,n= 5; green, dsRNAi,
n= 6; black, fjUP ,n= 4; magenta, fatRNAi,n= 5. Curves are vertically shifted by 10−4min−1for clarity.
42

F. Bosveld et al. - Supporting Online Material
5.2 Supporting movie captions
Movie S1. Drosophila pupa dorsal thorax tissue expressing E-Cad:GFP to label apical cell junctions,
imaged by multi-position confocal microscopy (24 positions at a 5 min time resolution) between 11 and
35 hAPF. The boxed region, highlighting the scutellum, is magnified at the left. The positions of the
macrochaetae and of the midline are indicated by white circles and by a black dotted line, respectively.
Arrows indicate the A/P and M/L axes. For compression reasons, these images have half the resolution of
original movie.
43

F. Bosveld et al. - Supporting Online Material
Movie S2. Tracking of cell dynamics in the scutellum and the posterior scutum. Note that, in order to show
the full color code, the above still image is the last image of the movie. (A) Dorsal thorax tissue labeled with
E-Cad:GFP and imaged by multi-position confocal microscopy at a 5 min time resolution between 11:30 and
27:30 hAPF. (B) Tracking of cell trajectories. (C) Tracking of cell divisions, apoptoses and rearrangements.
Each cell is color coded according to the number of cell divisions that it undergoes during the movie: pink
for cells having divided once; blue for cells having divided twice; green for the third wave of division. Links
used to calculate cell rearrangement matrix (section 4.2) are shown as lines. Two cells which are in contact
in an image, and not in the next one, correspond to a lost link, plotted as a yellow line. Two cells which get
in contact in an image, and were not in contact in the previous one, correspond to a gained link, plotted as a
red line. Links involving a four-fold vertex are shown in lighter colours. Yellows zones indicate an apoptosis
or delamination (which we do not distinguish). Light blue cells indicate new cells that entered the field of
view. (C’) Blow up of the region delimited in C by a cyan square. Scale bars (A-C): 10 μm.
44

F. Bosveld et al. - Supporting Online Material
Movie S3. Local tissue flow, deformation rate and rotation rate measured on Movie S1. Left: flow velocity
is represented as arrows. Middle: deformation rate is represented as ellipses; a direction of elongation is
represented in red and contraction in blue. Right: rotation rate is represented by circle diameters; clockwise
is represented in red and counter-clockwise in blue. For compression reasons, only one image every half
hour is shown. Scale bars: 100 μm (black bars), 9×10−2μmmin
−1(arrow, left), 2.4×10−3min−1(blue
bar, middle), 8×10−5min−1(circle, right).
45

F. Bosveld et al. - Supporting Online Material
Movie S4. Scutellum labeled with D:GFP and Baz:mCherry during morphogenesis (11 to 26 hAPF). The
positions of the macrochaetae and of the midline are indicated by yellow circles and by a cyan dashed line,
respectively. Arrows indicate the A/P and M/L axes.
46

F. Bosveld et al. - Supporting Online Material
Movie S5. Representative movies of cell junction ablations with high (left) or low (right) D:GFP signal in
the scutellum of pupae expressing D:GFP and Baz:mCherry.
47

F. Bosveld et al. - Supporting Online Material
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