© 2015. Published by The Company of Biologists Ltd | Development (2015) 142, 692-701 doi:10.1242/dev.116533
RESEARCH ARTICLE
Force production and mechanical accommodation during
convergent extension
ABSTRACT
Forces generated within the embryo during convergent extension (CE)
must overcome mechanical resistance to push the head away from the
rear. As mechanical resistance increases more than eightfold during CE
and can vary twofold from individual to individual, we have proposed that
developmental programs must include mechanical accommodation in
order to maintain robust morphogenesis. To test this idea and investigate
the processes that generate forces within early embryos, we developed
a novel gel-based sensor to report force production as a tissue changes
shape; we find that the mean stress produced by CE is 5.0±1.6 Pascal
(Pa). Experiments with the gel-based force sensor resulted in three
findings. (1) Force production and mechanical resistance can be
coupled through myosin contractility. The coupling of these processes
can be hidden unless affected tissues are challenged by physical
constraints. (2) CE is mechanically adaptive; dorsal tissues can increase
force production up to threefold to overcome a stiffer microenvironment.
These findings demonstrate that mechanical accommodation can
ensure robust morphogenetic movements against environmental and
genetic variation that might otherwise perturb development and growth.
(3) Force production is distributed between neural and mesodermal
tissues in the dorsal isolate, and the notochord, a central structure
involved in patterning vertebrate morphogenesis, is not required for force
production during late gastrulation and early neurulation. Our findings
suggest that genetic factors that coordinately alter force production and
mechanical resistance are common during morphogenesis, and that
their cryptic roles can be revealed when tissues are challenged by
controlled biophysical constraints.
KEY WORDS: Morphogenesis, Mechanotransduction, Gastrulation,
Notochord, Cell and tissue mechanics, Rho Kinase, Viscoelasticity
INTRODUCTION
Convergent extension (CE) is a major contributor to the
morphogenetic movements that physically shape the early vertebrate
embryo. During CE, dorsal embryonic tissues progressively deform
themselves and elongate the whole embryo along the anterio-posterior
(AP) axis while narrowing in the mediolateral (ML) direction (Keller
et al., 2003). From a mechanical perspective, the degree of
deformation must be proportional to active forces, which drive the
tissue deformation, and must be inversely proportional to passive
tissue mechanical properties such as stiffness, which resist
deformation. Previous studies indicated that the stiffness of the
1
Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA 15213,
2
USA. Department of Developmental Biology, University of Pittsburgh, Pittsburgh,
3
PA 15213, USA. Department of Computational and Systems Biology, University of
Pittsburgh, Pittsburgh, PA 15213, USA.
*Present address: Department of Pulmonary Medicine, Zhongshan Hospital, Fudan
University, Shanghai 200032, China.
‡
Author for correspondence ([email protected])
Received 12 August 2014; Accepted 19 December 2014
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dorsal tissues increased eight- to tenfold over the course of CE (Zhou
et al., 2009); yet, these same tissues maintain a nearly constant
elongation rate. Another finding from that same study revealed that
both whole embryos and dorsal tissue isolates cultured in a Rho kinase
(ROCK) inhibitor could also maintain constant elongation rates
indistinguishable from controls. These findings raised a number of
questions concerning the regulation of force and mechanical
resistance during CE and whether the two processes are coupled.
Mechanical considerations such as these suggest that the bulk
tissue elongation forces should match the changes in tissue stiffness
(Davidson et al., 2009). The coordination of force production with
the local mechanical environment could be accomplished through
a variety of mechanisms, ranging from purely mechanical feedback
to mechanosensing and signaling pathways (Schwartz and
DeSimone, 2008; Zhou et al., 2010; Miller and Davidson, 2013).
Alternatively, dorsal axial tissues might ignore signals from their
external mechanical environment and generate the same amount of
force regardless of the stiffness of the rest of the embryo. Given the
importance of these issues to the successful outcome of
morphogenesis, it is surprising that the molecular or physical
processes that balance force-to-mechanical resistance, or provide
mechanical accommodation during morphogenesis, are largely
unknown.
To understand whether force production and mechanical
resistance are coupled requires the ability to quantify force
production within the embryo. Yet, few direct mechanical
measurements of force production by embryonic tissues are
available to test whether force production is independent of the
local microenvironment or whether mechanosensing and signaling
feedback networks operate. Thus, in order to understand how force
and stiffness are coordinated in multicellular tissues we first need to
reliably quantify these forces.
Several techniques have been used to directly measure the bulk
forces generated during morphogenesis. In one study, a fiber optic
system was demonstrated that could measure the elongation force of
a Keller sandwich explant made from Xenopus laevis frog dorsal
marginal zone tissues (Moore, 1994). Another study used a pair of
parallel wires glued to the superficial ectoderm to measure tension
forces within the early neural plate of Ambystoma mexicanum
embryos (Benko and Brodland, 2007). The forces needed to stall
neural fold closure in two amphibian species, Triturus alpestris and
A. mexicanum, have been estimated with magnetically manipulated
steel ‘dumb-bells’ (Selman, 1955, 1958). All of these biophysical
approaches require dedication of specialized equipment, micromanipulated optical fibers, thin wire force transducers or magnetically
controlled steel dumb-bells to measure force production within a
single embryo or tissue explant for extended periods of time. Such
approaches provide insights into the physical constraints of
morphogenesis but are not well suited to complex analyses of the
molecular and mechanical coordination of force production during
morphogenesis.
DEVELOPMENT
Jian Zhou1, *, Siladitya Pal1, Spandan Maiti1 and Lance A. Davidson1,2,3,‡
RESEARCH ARTICLE
Development (2015) 142, 692-701 doi:10.1242/dev.116533
For these reasons we developed a new tool to measure tissue-scale
force production and investigated the mechanical control of
elongation during convergent extension.
We report here the development and application of a reliable
technique to measure force production by converging and extending
dorsal tissues microsurgically isolated from gastrulating X. laevis
embryos. Using this technique, we reveal cryptic changes in force
production that balance altered tissue stiffness and suggest that
mechanical feedback at the tissue level is in part responsible for
robust convergent extension movements. Furthermore, we
demonstrate that the notochord plays at best a minimal role in
driving axial elongation, whereas the primary contributors to force
production during elongation are the neural plate, the medial-most
paraxial mesoderm and more posterior dorsal tissues.
RESULTS
Fig. 1. Gel force sensor. (A) Schematic of gel force sensor shows a dorsal
isolate embedded in agarose gel with fluorescent beads. A confocal optical
stack is collected near the mid-plane of the tissue to detect the gel deformation.
(B) When tissues converge in mediolateral (ML) direction and extend along the
anterio-posterior (AP) axis, they compress the gel at the AP ends of the isolate.
(C) Flow chart of the procedure for computing elongation forces. (D) As tissue
extends, the immediately surrounding gel (black) is deformed and the
deformation tracked (blue) by embedded fluorescent beads at time=0 (red) and
after 4 h (green). (E) The beads closest to the ends of the tissue along the AP
axis (dashed box in D) are the most displaced.
coming to equilibrium against the constraining agarose gel (see
supplementary material Movie 2). To further confirm the ability of
the gel to capture the time dependence of tissue elongation forces we
measured the forces generated by converging and elongating dorsal
isolates with stiffness-calibrated glass needles (supplementary
material Fig. S3). We further confirmed the gel sensor with
animal cap explants that are not known to undergo elongation, and
found that these tissues did not produce observable stress
(supplementary material Fig. S4). These tests demonstrate that gel
stress equilibrates with the forces produced by the explant.
Mapping forces of convergent extension using the gel force
sensor
Dorsal isolates undergoing CE deform the agarose gel at both
anterior and posterior ends (Fig. 3A-C) and lose contact with the gel
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DEVELOPMENT
To quantify the forces driving convergent extension we
developed a method to measure force using an agarose gel as a
force sensor. Agarose has been used to culture cells and tissues
and its mechanical properties have been extensively characterized
(Tokita and Hikichi, 1987; Ross and Scanlon, 1999; Normand
et al., 2000; Balgude et al., 2001; Gordon et al., 2003; Chen et al.,
2004; Zeng et al., 2006). We embedded microsurgically isolated
X. laevis embryonic tissues that include the dorsal anlagen
(referred to here as the dorsal isolate) in ultra-low-gelling
temperature agarose in a fluid state at room temperature (RT)
(Fig. 1A). Cooling the fluid agarose to 14.5°C causes the agarose
to solidify around the dorsal isolate. Immediately after gelling, the
solid agarose immobilizes the explant, but as the dorsal isolate
generates force it pushes on and deforms the surrounding gel
along the AP axis (Fig. 1B). Agarose holds the tissue in place and
acts as a force sensor. To determine forces generated by the
extending dorsal isolate we calculated the forces needed to
displace the gel (Fig. 1C). To calculate those forces we first
obtained a map of gel displacement by tracking the movement of
small fluorescent beads embedded in the gel (Fig. 1D). The beads
closer to the AP ends of the tissue moved more than 20 µm
(Fig. 1E), whereas beads further from the tissue showed little
displacement. From the displacement field and the mechanical
properties of the agarose gel obtained using a rheometer we
computed the stress field surrounding the elongating tissue. In
order to validate the operation of the agarose gel as a force sensor
we carried out a series of tests (see supplementary material
methods), confirming the precision of our strain measurements
(supplementary material Fig. S1) and the accuracy of the stress
calculations (supplementary material Fig. S2).
In order to confirm that the agarose gel was not simply tracking
tissue displacements but rather reporting forces produced by the
explant, we investigated the changing stress levels as an embedded
tissue elongated. Confocal stacks of bead positions were collected at
1-h intervals and their displacements calculated (Fig. 2A). From
these displacements we calculated stress in the gel (Fig. 2B),
maximal displacement of the gel at the AP ends (Fig. 2C), mean
stress (Fig. 2D) and stress profiles (Fig. 2E). The stresses at the
anterior and posterior ends of the explants are directed normally to
the surface of the gel. The mean stress was computed as the average
stress value of stress immediately surrounding the anterior or
posterior ends of explants. Furthermore, high AP-directed stresses at
the AP ends of the explant are mainly compressive (balancing
tensional stresses in the gel are typically low but can be observed at
the mediolateral face of the explant, see supplementary material
Fig. S6A). These observations reveal the explant extending and
RESEARCH ARTICLE
Development (2015) 142, 692-701 doi:10.1242/dev.116533
Fig. 2. Rate of stress production by a dorsal isolate. (A) Bead
positions at end of dorsal isolate before deformation (time=0 h), and 2
and 4 h later. The dorsal isolate (asterisk) is outlined (white line).
(A′) Bead displacements between 0 (red) and 4 h (cyan) shown in
overlay of the region in the dashed box in A. Dark-blue lines connect
beads at 0 and 4 h. (B) von Mises stress calculated in the gel shown in
A at 0, 2 and 4 h. (C) Maximal bead displacements in the AP
direction over time. (D) Increasing maximal stress (σmax) of the dorsal
isolate. (E) Profile of stress across the AP face of the isolate
calculated at 2 and 4 h. The profile is approximately centered on the
dorsal midline of the isolate.
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found that DV thickening produced stresses comparable to AP
elongation. By checking the displacement map, we found that gel
deformation along the AP axis was focused along the anterior and
posterior axes (Fig. 3H and supplementary material Fig. S7B),
whereas deformation by thickening was located along dorsal and
ventral faces (Fig. 3K and supplementary material Fig. S7B). There
was minimal gel displacement along the DV direction at anterior
and posterior ends (supplementary material Fig. S7), caused by
either tissue elongation or thickening. Positioning a dorsal isolate so
that the ML and DV axes were aligned with the confocal plane
(Fig. 3J) revealed tissue thickening forces produced at the midpoint
of the AP axis (Fig. 3K,L). By positioning dorsal isolates in
different orientations we are able to extend our two-dimensional
(2D) stress maps to visualize the three-dimensional (3D)
distribution of stress produced during CE.
CE force production is regulated by myosin II contractility
With a robust tool to measure stress production we investigated the
regulation of AP elongation forces by myosin II contractility.
Dorsal axial tissue explants elongate ∼40% over 5 h without any
physical constraints (Fig. 4A,B). As a previous study had shown
that the ROCK inhibitor Y27632 greatly reduces tissue stiffness
along the AP axis (Zhou et al., 2009), we expected that it would
also affect rates of convergent extension; however, we found no
significant difference of elongation rates (Fig. 4B). To test
whether force production was coupled to tissue stiffness, we
embedded dorsal isolates in agarose gel with Y27632 and
found that their elongation rate was reduced (Fig. 4A,B), and
that they produced lower maximal stress (Fig. 4C,D; mean σmax of
control and Y27632-treated tissues were 5.0±1.6 Pa and
1.4±0.7 Pa, respectively) and lower mean von Mises stress (<σ>;
Fig. 4G). Thus, we conclude that lowered ROCK and myosin
activity coordinately reduces both bulk stiffness and bulk force
production, thus allowing unconstrained dorsal isolates to elongate
at the same rate as untreated dorsal isolates. Surprisingly, reduced
force production after ROCK inhibition is only revealed when
isolates are challenged to elongate against the mechanical
constraints of the agarose gel.
DEVELOPMENT
along the mediolateral sides (Fig. 3B,B′). The displacement of the
gel is reported by registration of two images, one taken shortly after
the explant is immobilized and one 4 h later (Fig. 3D). We assumed
there were no stresses present in the gel at the start of the experiment
and calculated stress within the gel in its final, deformed state. From
the bead displacement maps and the viscoelastic properties of
agarose gel we used a commercially available finite element (FE)
solver to compute the equivalent or von Mises stress [σ; Fig. 3E; see
Fischer-Cripps (2007)]. Von Mises stress, which we subsequently
refer to as ‘stress’, is commonly used to indicate the total stress
present in a material. However, we can also represent the forces
produced by elongating dorsal isolates with strain energy density
(supplementary material Fig. S5A) or maximum principal stress
(supplementary material Fig. S5B-D), or directly calculate the strain
in the gel (supplementary material Fig. S6).
Embedded dorsal isolate tissues extend for more than 4 h in
the gel and produce a maximum stress (σmax) up to 7 Pa (Fig. 3E)
along the mediolateral axis. The maximum stress always
colocalizes with the mediolateral midline of the dorsal isolate
(Fig. 3E), suggesting that the notochord and surrounding paraxial
mesoderm tissues extend faster and produce larger forces
compared with the other tissues. We routinely found that
posterior ends produce a higher, more medially focused pattern
of stress than that of the anterior end (Fig. 3E,F), even though we
found no significant difference comparing the maximum or mean
stress between the two ends. We note that stresses, unlike net
forces at the ends, do not need to balance, as the areas and
distribution of stresses are not uniform.
Using our gel force sensor, we are also able to quantify stress
produced by tissue thickening (Keller et al., 2008) along the dorsoventral (DV) axis by simply changing the orientation of the dorsal
isolate in gel. In the case described above, the dorsal isolate was
positioned in the gel, with the ML axis and AP axis aligned with the
plane of the confocal section (Fig. 3A). Alternatively, by
positioning the dorsal isolates with their DV axis and AP axis
aligned with the plane of the confocal section (Fig. 3G), we can
measure displacement and stress in the gel produced by elongation
and dorsal ventral thickening (Fig. 3H and I, respectively). We
RESEARCH ARTICLE
Development (2015) 142, 692-701 doi:10.1242/dev.116533
CE mechanically accommodates to stiffer
microenvironments
From previous studies of mechanical feedback in single cell mechanics
[e.g. Discher et al. (2005)] we suspected that increasing the stiffness of
mechanical microenvironment would increase the elongation forces
generated by dorsal isolates. Our gel-based force sensor allows us to
change the mechanical environment by simply altering the
concentration of the embedding agarose gel. To determine the
effects of mechanical environment on the force production of dorsal
axial tissues, we measured force production by explants embedded in
agarose gels with three different concentrations (0.6%, 0.9% and
1.2%), the elastic moduli of which were typically 30, 200 and 500 Pa,
respectively. We found that dorsal isolates embedded in 200 or 500 Pa
gels generated greater stress than those embedded in 30 Pa gels
(Fig. 5A-C). Both the σmax and <σ> produced by dorsal isolates in the
0.6% gel were significantly lower than those in stiffer gels (Fig. 5D-F).
Comparisons between the stress produced in 0.9% and 1.2% gels are
challenging, as stiff gels introduce higher background noise, due to the
combination of high stiffness gel and small inaccuracies in measuring
gel displacements. Thus, dorsal isolates can generate larger stresses
when faced with a stiffer microenvironment. These results suggest that
mechanical feedback produces greater stress to overcome larger
mechanical constraints of the surrounding gel.
Many sources of mechanical feedback have been proposed to
regulate embryogenesis, ranging from intra-molecular changes in
conformation to multi-protein mechanochemical signaling networks
(Mammoto and Ingber, 2010; Miller and Davidson, 2013). However,
to understand how such a feedback network might operate we sought
to model the basic mechanics of a converging and extending tissue
surrounded by a passively compliant material. Using an FE model
we simulated a dorsal isolate with a morphology sampled from a
representative explant (Fig. 5G) embedded within an agarose gel
(Fig. 5H). To mimic the mechanics of convergent extension
we implemented a mediolaterally oriented contractile stress (see
Materials and Methods) and calculated the effects of AP elongation on
stress in the surrounding gel. The qualitative pattern of von Mises stress
in the model matches stress patterns of dorsal isolates embedded in
agarose gels. We could match the stress magnitude to observed
levels by adjusting the maximum contractile stress to 15 Pa (compare
Fig. 5I with Fig. 3E). Next, we increased the model stiffness of the
surrounding gel to 200 and 500 Pa and calculated the stress produced
by the same internally generated mediolateral stress (Fig. 5J,K). We
found that stress profiles across the AP face of simulated dorsal isolates
were similar to those observed experimentally (compare simulated
stress in Fig. 5L with measured stresses in Fig. 5D). Thus, increased
stress production in response to increased physical constraint can be
attributed to the maintenance of constant levels of mediolateral
contraction within the elongating tissue.
Confinement in stiffer environment alters tissue architecture
As dorsal isolates confined in gels do not extend as much as ‘free’
isolates we tested whether the internal architecture of axial and
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DEVELOPMENT
Fig. 3. Mapping forces of convergent extension using the gel force sensor. (A) An elongating dorsal isolate is positioned in agarose gel, with the ML axis and
AP axis aligned with the plane of the confocal section. (B) Dorsal isolate is embedded in gel (dorsal view) at time=0. (B′) When the isolate extends, it deforms
the agarose gel at both its anterior and posterior ends. As the isolate converges, it loses contact with the gel along its ML sides (arrows). (C) Beads within the gel
are visible in the ‘null force’ (red) and ‘force-loaded’ (green) states. Note: some green beads (asterisk) ‘appear’ at 4 h. These are not due to deformation but
become visible because they are no longer obscured by converging tissues. (D) Gel displacements are calculated by image registration of the two images in C and
drawn as arrows. (E) Stress distribution computed using an FE model shows that the posterior end produces a higher, more axially focused pattern of stress than
that of the anterior end (F). (G) Dorsal isolates positioned with their DV and AP axes aligned with the plane of the confocal sections. (H) Stress produced by
both the tissue elongation forces in AP axis and dorsal ventral thickening forces in DV axis. (I) Gel displacement in AP axis caused by tissue elongation is focused
along the anterior and posterior axis. (J) Gel displacement in DV axis caused by tissue thickening is located at dorsal and ventral sides. There is no gel
displacement along the DV direction at anterior and posterior ends caused by either tissue elongation or thickening. (K) Dorsal isolates positioned with their DV
and ML axes aligned with the plane of the confocal section. (L) Stress produced by tissue thickening forces at a point midway down the AP axis. The arrow lengths
in D, H and K indicate a tenfold distance of the actual gel displacement. See supplementary material Fig. S7 for contour maps of displacements.
RESEARCH ARTICLE
Development (2015) 142, 692-701 doi:10.1242/dev.116533
Fig. 4. Elongation stress production but not unconstrained deformation is regulated by myosin II contractility. (A) Dorsal isolates elongate more in DMSO
and 40 µM Y27632 without mechanical constraint than they elongate after being embedded in agarose gel. (B) Tissues elongate at same rates in DMSO or
Y27632 without mechanical constraint and elongate much less in Y27632 when embedded in gel. (C,D) Stress field surrounding isolates cultured in DMSO (C) or
Y27632 (D) over 4 h. (E) Stress distribution along the anterior and posterior ends of the DMSO and Y27632-treated isolates. (F,G) Both the maximum stress
(F) and mean stress (G) of the extending isolates in DMSO were significantly greater than those of isolates in Y27632. Significance of stress measurements
among multiple clutches were calculated using two-way ANOVA (*P<0.05; **P<0.01; ***P<0.005). Error bars in B, F and G indicate s.d.
Notochord does not contribute to force production
The formation of a knob at the posterior end of the notochord
suggested that notochord shear or extrusion might be responsible for
the asymmetric stress patterns observed at the posterior end of
elongating dorsal isolates and that the notochord contributes to force
production. To test the contribution of the notochord to force
generation, we compared the forces produced by dorsal isolates from
which the notochord was excised with force produced by mockoperated dorsal isolates. The mock control and notochord-less dorsal
isolates (Fig. 6A) were microsurgically prepared as described
previously (Zhou et al., 2009) and their architecture confirmed by
confocal sections of stained fibronectin fibrils (Fig. 6A′,B′). We
found that notochord-less dorsal isolates embedded in 30 Pa gel
generated a similar magnitude and pattern of force compared with
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mock control dorsal isolates (Fig. 6C); the mean values of σmax
produced by mock control and notochord-less dorsal isolates were
4.5±1.1 Pa and 4.1±1.7 Pa, respectively (Fig. 6C). We found no
significant difference in σmax or <σ> between mock control and
notochord-less dorsal isolates (Fig. 6D,E). Thus, the notochord is
unlikely to contribute to the magnitude and patterning of the forces
driving tissue elongation during late gastrulation and early
neurulation.
Paraxial mesoderm, the posterior half of the dorsal isolate
and the neural plate are major contributors to elongation
forces
To test the relative contribution of other tissues within the dorsal
isolate we created a series of explants from pieces of the dorsal
isolate. After we confirmed the capacity of the explants to elongate
we measured their force production capacity. First, we compared the
stress produced by axial and paraxial (medial-notochord-medial;
MnM) and lateral plate mesoderm (LL) using explants described
previously (Zhou et al., 2009). MnM explants produced significantly
higher σmax and <σ> than the LL explants (supplementary material
Fig. S9). Next, we compared the force production of anterior and
posterior halves with intact dorsal isolates (Fig. 7A). We note that
anterior and posterior halves elongate to the same degree
(supplementary material Fig. S10; Movie 3). Anterior halves
produced significantly lower σmax and <σ> than the full dorsal
isolate, whereas stress production by the posterior halves could not
be distinguished from either anterior halves or the full dorsal isolate
(Fig. 7B,C). In both cases the fragments of the dorsal isolate that
contain the most paraxial mesoderm produce the greater stress.
However, the dorsal isolate consists of both neural and mesodermal
tissues, and both tissues are known to elongate in isolation (Elul
et al., 1997; Poznanski et al., 1997; Keller et al., 2000). As the neural
plate in Xenopus is only two cells thick, we utilized a neural plate
‘sandwich’ (NS) explant created from two neural plates isolated from
DEVELOPMENT
paraxial tissues were altered after gel confinement. To check the
architecture of dorsal axial tissues for irregular development, we
fixed unconfined and gel-bound isolates, stained fibronectin, and
collected confocal sections. The projections of fibronectin fibrils
show that dorsal isolates embedded in stiffer gels were wider and
included a curved notochord with a ‘knob-shaped’ posterior end
(supplementary material Fig. S8A-C) compared with dorsal isolates
cultured without mechanical restriction (supplementary material
Fig. S8D). (Note: other aspects of morphogenesis in dorsal isolates,
including neural tube closure, are not perturbed in gel-confined
explants or gel-confined whole embryos; see supplementary
material Movie 1.) Knob-ended notochords could have been
caused by shear movements between the notochord and adjacent
paraxial mesoderm (Wilson et al., 1989; Keller et al., 1992), and
suggested that the shear stresses between the notochord and adjacent
paraxial mesoderm might play a role in generating force during CE.
Curved notochords also suggested dorsal axial tissues might
undergo Euler buckling as they extend and narrow within the
confines of the agarose gel.
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Development (2015) 142, 692-701 doi:10.1242/dev.116533
embryos at mid- to late-gastrula stages (st. 11.5-12; Fig. 7D). The two
explants were held together at their deep cell interface for 30 min
until free-epithelial edges resealed. NS explants elongate at the same
rate as dorsal isolates (supplementary material Fig. S11; Movie 4)
and are easily confined within agarose force-reporting gels.
However, due to the thin form of the NS they frequently buckle
within the constraining gel after elongating more than 3 h. Thus, we
restricted analysis to NS stresses produced within 2 h after
embedding. We found that the NS explant generated levels of
stress similar to those produced by the dorsal isolates (Fig. 7E-H;
P=0.4 and P=0.6 for σmax after 1 and 2 h, respectively). With their
large contribution to the cross-section of dorsal tissues and their
similar levels of stress production, we conclude that the stress
production by paraxial mesoderm and prospective neural tissues
contribute equally to elongation within dorsal tissues.
DISCUSSION
To investigate force production and mechanical accommodation
during convergent extension we developed an innovative method to
reliably measure the elongation force generated by dorsal tissues
between late gastrula and early neural tube stages. The agarose gel
force sensor enables analysis of force production during CE and
might be used to measure force production by other elongating
tissues, of which there are many in animal development. The nonadhesive gel-based sensor has several advantages over the previous
methods for measuring forces produced during morphogenesis:
(1) a gel can hold a tissue without drift as the tissue extends and
changes its shape; (2) measurement of forces produced by multiple
explants in a single gel allows higher throughput than cantileverbased methods; and (3) the gel force sensor can be adapted to
measure a wide range of forces by tuning the elastic modulus of the
agarose gel. Furthermore, more complex hydrogels can be
formulated with ECM protein fragments or custom time-release
growth factors to instruct programs of morphogenesis (Lee and
Mooney, 2001). Although our technique is designed to measure
uniaxial elongating forces of dorsal tissues, gel-based force sensors
could also be used to measure forces produced by other tissues that
extend or grow irregularly.
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DEVELOPMENT
Fig. 5. Dorsal isolates in stiffer gel
produced greater force: experiment and
model. (A-C) Stress maps of dorsal
isolates embedded in 30-Pa gel (A), in 200Pa gel (B) and in 500-Pa gel (C). (D) Stress
distribution along the midline axis of dorsal
isolates embedded in gels with different
elastic modulus. (E,F) Both the maximum
stress (E) and mean stress (F) of the dorsal
tissues in a 30-Pa gel are significantly less
than those of tissues in 200-Pa or 500-Pa
gels. Significance of stress measurements
among multiple clutches were calculated
using a two-way ANOVA (*P<0.05;
**P<0.01; ***P<0.005). Error bars in E,F
indicate s.d. (G) Elongation stress
simulated in a sample dorsal isolate. (H) FE
grid surrounding the isolate. Higher
densities of the elements were used within
the isolate and near its surface. (I-K) Stress
fields produced from constant ML stress in
a 30-Pa dorsal isolate within a 30-Pa elastic
gel (I), a 200-Pa elastic gel (J) and a 500-Pa
elastic gel (K). (L) The stress profiles across
the face of the simulated elongating isolate
show increasing stress in stiffer gels.
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Development (2015) 142, 692-701 doi:10.1242/dev.116533
We applied the gel-based sensor to measure the elongation force
produced by dorsal axial tissues. Physical constraints of the gel can
prevent some natively occurring large-scale movements, e.g.
blocking some aspects of tissue folding, and also induce tissue
buckling that would not normally occur. For instance, we routinely
observed bending by thin neural plate sandwiches, reminiscent of
Euler buckling, as these tissues elongated. Dorsal tissues generated
stresses of 5.0±1.6 Pa on the surrounding gel, whereas animal cap
tissue explants generated stresses of 0.3±0.1 Pa. The production of
stress by a dorsal isolate is often asymmetric; the posterior faces of
dorsal isolates produced slightly higher stress than the anterior end
due to the smaller cross-sectional area of the posterior end where it
contacts the agarose gel (Fig. 3C) (Wilson et al., 1989; Keller et al.,
1992). Physical principles dictate that elongation forces must
balance at the two ends but stresses do not need to balance. As force
is the product of stress and area, the posterior directed stress can be
larger than the anterior due to differences in the distribution of stress
or differences in the surface areas of the two faces.
We find no significant difference between stress produced by
mock-operated and notochord-removed explants. A tissue must
meet certain requirements to generate force for axis elongation:
certain length, width and thickness. Both the neural epithelium and
paraxial mesoderm meet those requirements. By contrast, the
notochord after stage 12 has completed mediolateral cell
intercalation and presents too small a cross-sectional area to
generate large forces. The most parsimonious interpretation of
these results is that notochord does not contribute significantly to
the force production. We might speculate that the embryo
compensates for the removal of notochord; however, such a new
mechanism would require added levels of mechanosensing and
response by paraxial tissues, which we are not able to exclude. We
would not dispute that the notochord plays a mechanical role to
straighten the tail-bud stage embryo but that a mechanical role
during axis elongation is unlikely.
698
Previous biomechanical analyses of gastrula stages in Xenopus
embryos (Beloussov et al., 2006; Zhou et al., 2009, 2010; von
Dassow et al., 2010, 2014; Luu et al., 2011) have suggested that
mechanical feedback mechanisms operate during development to
allow robust morphogenetic movements. Force production in dorsal
tissues is needed to deform both those tissues and the rest of the
embryo. Once removed from the embryo, forces acting within the
dorsal isolate still carry out work to deform the dorsal isolate. It is
tempting to suggest that all stiffness in the embryo is produced by
mechanical contractility and that reduction in force production seen
with ROCK inhibition exactly matches reduction in stiffness. Such
coupling might operate cell-autonomously, for instance by coupling
force production to tissue stiffness via myosin II contractility. This
mechanism is qualitatively compatible with our observation that
elongation forces of dorsal tissues were significantly decreased
when myosin II contractility was reduced. However, myosin II
contractility does not account for all stiffness within embryonic
tissues; disruption of contractility by Y26732 reduces Young’s
modulus by 40-60% at stage 16 (Zhou et al., 2009), and we observe
an 80% reduction in stress production. Furthermore, it is unclear
whether feedback or mechanical coupling operates over longer
distances, for instance coordinating ML tensile stress within adjacent
neural and paraxial mesoderm cells when these tissues differ in
stiffness or as tissues stiffen during the course of gastrulation. A wide
range of mechanosensing and mechanotransduction pathways have
been identified in cultured adult cells [e.g. by Discher et al. (2005)],
yet few of these feedback systems have been rigorously tested in
developing embryos. How these mechanical processes are triggered
and coordinated, and how ‘mechanical’ information is sensed and
passed from cell to cell in the embryo remains unknown.
These studies raise several interesting questions regarding the roles
of mechanical adaptation and accommodation in morphogenesis.
There has been little agreement in the field of mechanobiology over
the use of the term ‘adaptation’. Many usages simply reflect the
DEVELOPMENT
Fig. 6. Contribution of the notochord to
force production. (A) Mock-operated
control dorsal isolates were split axially and
then re-combined. (B) Notochord was
microsurgically removed along notochordparaxial mesoderm boundary to produce
notochord-less dorsal isolates.
(A′) Representative average projections
and transverse maximum projections of
confocal sections of stained fibronectin
fibrils of mock control and notochord-less
dorsal isolates (B′) show that the mock
control dorsal isolate contains neural
ectoderm (ne), notochord (n), paraxial
mesoderm (s) and endoderm (e), whereas
the microsurgically prepared notochordless dorsal isolate lacks a notochord
( posterior, p; anterior, a). (C) Stress
distribution along the midline axis of mock
control and notochord-less dorsal isolates.
(D,E) Both the maximum stress (D) and
mean stress (E) of the mock control and
notochord-less dorsal isolates are not
significantly different. Significance of stress
measurements among multiple clutches
were calculated using two-way ANOVA
(*P<0.05; **P<0.01; ***P<0.005). Error
bars in D,E indicate s.d.
RESEARCH ARTICLE
Development (2015) 142, 692-701 doi:10.1242/dev.116533
Fig. 7. Posterior axial tissues and neural plate are additional sources of force production. (A-C) The dorsal isolate can be bisected into a posterior and
anterior half for measurement of stress production. Anterior and posterior dorsal isolate halves extend equally well (see supplementary material Fig. S10 and
Movie 3). The anterior half of the dorsal isolate produces lower normalized maximum stress (B) and normalized mean stress (C) than the full-sized dorsal isolate.
Posterior halves typically produce less stress than the full-sized dorsal isolate, but this difference is not statistically significant. (D) Two neural plates can be
recombined to produce a single neural sandwich (NS). Neural sandwiches extend as well as dorsal isolates (see supplementary material Fig. S11 and Movie 4).
(E-H) Normalized maximum (E,G) and mean stress (F,H) production in neural sandwiches is variable but no significant differences were detected after 1 h of
elongation (three clutches) or after 2 h (two clutches). Significance of stress measurements among two clutches were calculated using two-way ANOVA
(*P<0.05). Error bars indicate s.d.
MATERIALS AND METHODS
Embryo and tissue preparation, histology,
immunocytochemistry and confocal microscopy
X. laevis embryos were obtained by standard methods (Kay and Peng, 1991),
fertilized in vitro, dejellied in 2% cysteine and cultured in 1/3× MBS (Sive et
al., 2000) at 14.5-21°C to stage 16 (Nieuwkoop and Faber, 1967). Before
creating explants, vitelline membranes of embryos were removed with
forceps (Fine Science Tools) and transferred in DFA media [Danichik’s For
Amy; Sater et al. (1993)]. Dorsal axial tissues, neural sandwiches and animal
cap tissues were microsurgically dissected from embryos using hair loops
and hair knives. To stain fibronectin fibrils, explants embedded in agarose
gel were fixed in 3% TCA in 1× PBS (Davidson et al., 2004), stained with
mAb 4H2 (Ramos and DeSimone, 1996) against Xenopus fibronectin
(1:500) and visualized with a rhodamine-conjugated goat anti-mouse IgG
antibody (Jackson ImmunoResearch). After staining, the dorsal axial tissues
were dehydrated in methanol and cleared in Murray's clear (Davidson et al.,
2004). Single optical sections and z-series of explants were collected with a
confocal laser scan head (SP5, Leica Microsystems) mounted on an inverted
compound microscope (DMI6000, Leica Microsystems) using image
acquisition software (LASAF, Leica Microsystems). Average projection
and reslicing of z-series stacks was obtained with ImageJ (v. 1.38, Wayne
Rasband, NIH). Experiments involving X. laevis embryos were performed
under a protocol approved by the University of Pittsburgh Institutional
Animal Care and Use Committee (PHS Assurance Number: A3187-01).
Force measurement with agarose gel
Gel preparation
To measure the tissue elongation forces, dorsal axial tissues were embedded
in non-adhesive agarose gel. Briefly, ultra-low-gelling temperature agarose
(type IX-A; Sigma) was dissolved in DFA solution at 65°C and cast in a
13×10×6 mm chamber. The molten gel was cooled to RT and remained
liquid. Red FluoSpheres (580/605; absorption/emission wavelength in nm;
Invitrogen) were evenly dispersed in the liquid solution as markers to track
the gel deformation. Tissue explants were prepared and allowed to heal for
20 min to clear debris. The explants were then rinsed in fresh media and
transferred to the liquid gel at RT. Once tissues were positioned to allow
more than 1 mm separation between explants, walls of the chamber and
upper surface of the gel, the chamber was moved to a 14.5°C incubator to
699
DEVELOPMENT
observation of changes in force production in response to an altered
mechanical environment. A more stringent definition of adaptation
would require identification of mechanosensing pathways that
coordinate a defined mechanical response in the embryo. In this
study, we observed increased force production by dorsal isolates in
response to an increasingly stiff surrounding gel. However, after
developing a rather simple mechanical model we discovered
that increased force production did not necessitate complex
mechanosensing by embryonic tissues but could be understood as
a simple accommodation of a tissue that generates constant
ML tension. It is possible that mechanical adaptation might occur
during development but simpler mechanisms of mechanical
accommodation need to be excluded. Criteria for assessing
processes that maintain robust morphogenesis must include timedependent changes in geometry such as deformation analysis. As
deformation rates depend crucially on force production and
mechanical properties, efforts seeking to identify potential adaptive
pathways during morphogenesis must perturb these underlying
mechanics in a controlled manner and must be capable of evaluating
effects on both force production and mechanical properties. Analyses
of morphogenesis that limit their focus to deformation rates alone
might overlook processes that provide regulation and feedback that
enable robust morphogenesis.
There are technical and conceptual limitations of our force
measurement method. Technically, due to optically opaque tissue
we were unable to track gel deformation in all three dimensions.
Equilibrium stresses we report represent maximum stall forces. In
several cases, the maximum strain in the gel reached up to 20%,
which reduces the accuracy of our analysis. Lastly, whereas we can
formulate an agarose gel with a bulk elastic modulus to match the
residual Young’s modulus of the embryo, we cannot formulate a gel
to mimic the viscoelastic properties of embryonic tissues. Gels do
not undergo plastic deformation, and thus the elastic solid
mechanical properties of agarose limits the ultimate degree of
elongation for all tissues embedded in such gels.
RESEARCH ARTICLE
Mechanical properties of agarose gel
The mechanical properties of the agarose gels were measured to extract
parameters needed to model stress production in a FE model. We estimated the
maximum local strain in the gel domain induced by extending dorsal axial
tissues to be less than 20% over 5 h; the agarose gel is therefore modeled as a
linear viscoelastic material (Findley et al., 1989; Normand et al., 2000). We
measured the viscoelastic properties of the agarose gel by performing
oscillatory shear flow tests using a rheometer (AR2000; TA Instruments). The
bulk elastic modulus G′ (or storage modulus) and viscous modulus G″ (or loss
modulus) were measured in frequency sweep shear mode over 0.1 to 100 rad/
s. For viscoelastic parameters, the measured elastic modulus over this range of
frequencies was fitted with a two-mode linear viscoelastic model using
Mathcad software (v14, PTC), and then the extracted parameters (long-term
elastic modulus, elastic modulus at each mode and its corresponding
relaxation time) were used to build a Prony series to model the viscoelastic
material in FE model (Zeng et al., 2006). The long-term elastic modulus was
typically 30, 200 and 500 Pa for gels with concentration of 0.6%, 0.9% and
1.2%, respectively. The Poisson’s ratio of our agarose gels was assumed to be
0.5, based on a previous study (Normand et al., 2000).
Detecting gel deformation by image registration
To track the deformation in the gel domain, we adapted an algorithm which
registers two images by deforming one image of beads to match the other
(Sorzano et al., 2005). Red fluorescent beads (0.2 µm, 1 µm and 15 µm
diameter) were suspended in gel and scanned confocally using a
10× objective. A short confocal z-stack was collected near the dorsal
ventral mid-plane every 2 h and maximal projection of each z-series stacks
was obtained using ImageJ (NIH). Two maximal projection images of each
explant at different time points were aligned (Thevenaz et al., 1998) and
analyzed by the bUnwarpJ plug-in for ImageJ, which reported the
deformation between the two images as a vector field.
Using an FE model to calculate force production from experiments
When dorsal isolates are embedded and elongate in an agarose gel, they can
deform the gel in three possible directions: along the AP, ML and DV axes. By
changing the orientation of the dorsal isolate within the gel, we found minimal
displacement along the DV direction at either anterior or posterior ends,
indicating that the gel was primarily under compression in the AP direction.
Furthermore, dorsal isolates regularly extended only in the AP direction; thus,
we simulated tissue elongation as a 2D plane stress problem. We then
constructed a 2D FE model to compute the stress field in the gel based on the
displacement field and the viscoelastic properties of the gel. Briefly, 2D FE
meshes were generated with the free software TRIANGLE (version 1.6).
Triangular elements with same areas and refined angles are constructed based
on the real position of each bead reported by the bead tracking algorithm
(Sbalzarini and Koumoutsakos, 2005). Three-node linear plane stress triangle
elements (CPS3) were used for simulations. In our FE model, the gel domain
is assumed to be isotropic and linear viscoelastic. The displacement of the gel
was applied as a load through boundary conditions. The FE mesh, extracted
viscoelastic parameters of the agarose gel, initial conditions and displacement
boundary conditions of the gel served as input for the commercial FE software
package ABAQUS (Dassault Systems), and the stress distribution in the
agarose gel surrounding a sample was computed. The von Mises stress of each
node immediately surrounding the anterior and posterior ends of tissues was
extracted from the ABAQUS output files. The σmax and <σ> were calculated
for statistical analysis and color contours, plotted based on average values
within the elements. Typically, we found that stresses at the anterior and
posterior ends of the explant were directed normally to the surface of the gel.
Furthermore, all stresses in the gel were compressive.
Using FE model to calculate synthetic stress profiles
The 2D numerical simulations were performed with custom-made nonlinear
FE analysis software. An image of a representative tissue explant and gel was
700
used to generate the FE mesh using Cubit (v14.0, Sandia) mesh generation
software. A simulated explant was placed within gel (2.5×2.5 mm) and both
domains were discretized with four-noded quadrilateral elements. The explant
was discretized with 2149 nodes and 2064 elements, whereas the gel domain
was discretized with 5147 nodes and 4995 elements. A special four-noded
interface element (Maiti and Geubelle, 2006; Nittur et al., 2008) was used at
the interface between tissue explant and gel to account for the contact and
sliding between these two domains as well as separation during the course of
tissue elongation. Both the gel and explant were considered nearly
incompressible (Poisson’s ratio of 0.45) and neo-Hookean. The active stress
in the FE model acts along the mediolateral axis. For the explant, we kept the
material property (elastic modulus) constant with a value of 30 Pa (Zhou et al.,
2009). Active contractile stress within the simulated tissue was held constant
as the gel stiffness was increased from 30 to 200 and 500 Pa. To simulate force
production within the explant we used a time-ramped contractile stress of σact
(x,t)=σ0t/tmax with σ0=15 Pa along the medial lateral plane for all simulations.
The magnitude of σ0 was adjusted so that stress at the anterior and posterior
face of the simulated explant matched the stresses observed in 30-Pa gels.
Distribution of von Mises stress in the gel at the posterior face along the ML
plane near the interface between explant and gel was obtained at time t=tmax
when the contractile stress achieved its maximum value of 15 Pa.
Statistical analysis
Data were drawn from at least three separate experiments performed in
triplicate. The data are presented as mean±s.d. and analyzed using SPSS
version 16.0 statistical software. Two-way ANOVA, which includes
treatment and clutch as fixed and random factor, respectively, was used to
calculate the statistical difference of σmax and <σ> between treatments.
A P-value <0.05 was considered significant.
Acknowledgements
We would like to thank members of the Davidson lab, especially Drs Sagar Joshi,
Hye Young Kim and Michelangelo von Dassow for their comments and support
during these studies. Progress would not have been possible without the technical
assistance of Ms Lin Zhang. We thank Dr Sachin Velankar for training and use of his
AR2000 Rheometer.
Competing interests
The authors declare no competing or financial interests.
Author contributions
J.Z. and L.A.D. developed the approach, designed and performed the experiments,
and carried out data analysis. S.M., S.P. and L.A.D. developed the FEM model.
J.Z., S.P., S.M. and L.A.D. prepared and edited the manuscript for publication.
Funding
This work has been supported by grants from the National Institutes of Health (NIH)
[R01 HD044750; R21 ES019259] and the National Science Foundation (NSF)
[CAREER IOS-0845775; CMMI-1100515]. Any opinions, findings and conclusions
or recommendations expressed in this material are those of the authors and do not
necessarily reflect the views of the NSF or the NIH. Deposited in PMC for release
after 12 months.
Supplementary material
Supplementary material available online at
http://dev.biologists.org/lookup/suppl/doi:10.1242/dev.116533/-/DC1
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