Oscillatory cortical forces promote three dimensional cell intercalations that shape the mandibular arch

Multiple vertebrate embryonic structures such as organ primordia are composed of a volume of confluent cells. Although mechanisms that shape tissue sheets are increasingly understood, those which shape a volume of cells remain obscure. Here we show 3D mesenchymal cell intercalations, rather than cell divisions and biophysical tissue properties, are essential to shape the mandibular arch of the mouse embryo. Using a genetically encoded vinculin tension sensor, we show that cortical force oscillations promote these intercalations. Genetic loss and gain of function approaches show that Wnt5a functions as a spatial cue to coordinate cell polarity with cytoskeletal oscillation. YAP/TAZ and PIEZO1 serve as downstream effectors of Wnt5a-mediated actomyosin bias and cytosolic calcium transients, respectively, to ensure appropriate tissue form during growth. Our data support oriented 3D cell neighbour exchange as a conserved mechanism driving volumetric morphogenesis.


ABSTRACT
Multiple vertebrate embryonic structures such as organ primordia are composed of a volume of confluent cells. Although mechanisms that shape tissue sheets are increasingly understood, those which shape a volume of cells remain obscure. Here we show 3D mesenchymal cell intercalations, rather than cell divisions and biophysical tissue properties, are essential to shape the mandibular arch of the mouse embryo.
Using a genetically encoded vinculin tension sensor, we show that cortical force oscillations promote these intercalations. Genetic loss and gain of function approaches show that Wnt5a functions as a spatial cue to coordinate cell polarity with cytoskeletal oscillation. YAP/TAZ and PIEZO1 serve as downstream effectors of Wnt5a-mediated actomyosin bias and cytosolic calcium transients, respectively, to ensure appropriate tissue form during growth. Our data support oriented 3D cell neighbour exchange as a conserved mechanism driving volumetric morphogenesis.

INTRODUCTION
Morphogenesis refers to the process of shaping tissue during development, the reproducible nature of which is essential for appropriate pattern formation and function.
Most of the recognised principles of morphogenesis concern mechanisms that shape sheets of embryonic tissue 1-13 . In particular, exchange of cell neighbours is central to tissue shape change in two dimensions (2D) and involves a limited number of transient multicellular configurations including tetrads (T1 exchange) and rosettes. Actomyosin contractions generate forces that promote cell neighbour exchanges and are oriented, in part, by physical properties of tissue that may be anisotropic in nature [14][15][16] . Some of these principles have been extended to curved epithelial sheets by combining empirical and theoretical approaches [17][18][19] . However, it remains unclear whether similar mechanisms apply to mesenchymal tissues, in part because mesenchymal tissues have been regarded as less confluent due to the presence of abundant extracellular matrix in some contexts and to potentially less adherent cell-cell junctions 20 . Changes in the viscoelastic properties of tissue are also associated with, and may partly drive, morphogenetic movements [21][22][23][24] , although the relationship between cellular and tissue scale properties remains unclear and may be context-dependent.
Multiple organ primordia such as the branchial arches, limb buds and genital tubercle are composed of an internal bulk layer of mesenchyme. In models of multilayered vertebrate tissues such as the frog gastrula, mechanisms of morphogenesis include amoeboid endodermal cell movements 25 and mesodermal cell intercalations through junctional remodelling, though the latter takes place in a sheetlike manner 26,27 . Another example is elongation of the rod-like skeletal anlage in the vertebrate limb that is attributable to a highly structured columnar arrangement of chondrocytes embedded within abundant extracellular matrix and to oriented rearrangement of nascent daughter cells 28,29 . In contrast to these examples, very little is known about how more-or-less isotropic volumes of confluent cell organise to generate morphogenetic movements. For example, although the directional nature of mesodermal cell movements from the lateral plate to the limb bud has been demonstrated [30][31][32][33][34] , the cellular basis of those movements, and of volumetric morphogenesis in general, remain largely uncharacterised. 4 Early branchial arches are composed of a core volume of mesenchyme that is surrounded by a single cell layer epithelium. Although the neural crest [35][36][37] and cranial mesodermal 38 origins of branchial arch mesenchyme are well recognised, mechanisms by which the structure grows outward and acquires shape are less clear. Loss-offunction approaches that were intended to define the roles of various signalling pathways identified cellular processes that are relevant to branchial arch morphogenesis, such as cell survival [39][40][41][42][43] , cell proliferation 44,45 and cell migration [46][47][48] .
Those studies generated important insights, but were not intended to explain how the branchial arches acquire shape.
Craniofacial anomalies are common among birth defects. The mandibular portion of the first branchial arch generates multiple facial structures including the lower jaw, and some syndromes are associated with structurally common features of malformation such as a short (front to back) and broad (side to side) mandible. One of these, autosomal-dominant Robinow syndrome, is caused by mutations in components of the noncanonical WNT pathway including WNT5A and ROR2 [49][50][51][52] . Wnt5a mutant mice that phenocopy many of the features of the human syndrome exhibit a short and bulbous mandibular arch 50,53 , though the cellular and physical basis of the malformation is not clear.
Here we study the mandibular arch as a model of two distinct modes of 3D morphogenesis. We show that cell division and physical tissue properties are important for growth but do not sufficiently explain how the arch primordium acquires a narrow mid-portion and a bulbous distal portion. Our data support a model in which 3D mesenchymal cell intercalations narrow and elongate the mid-portion. Relatively high amplitude cortical force oscillations promote cell intercalations in a Wnt5a-and Piezo1dependent manner, implying these regulators spatially fine tune physical cell behaviours.

RESULTS
Spatial distributions of cell division frequency and viscoelastic tissue properties are insufficient to explain mandibular arch shape The first branchial arch buds at the ventral aspect of the midbrain-hindbrain boundary in the mouse embryo. As shown by optical projection tomography (OPT), the mandibular portion of the first branchial arch remodels from a rod-like structure at the 19 somite stage (~E9.0) to form a narrow central 'waist' and a distal bulbous region between somite stages 21-28 (~E9.25-E9. 75; Fig. 1A). In this study, we focused on the shape change between 19 and 21 somite stages (a ~4 h period) (Supplementary Mov. 1, 2) to understand how the waist and bulbous regions become defined.
To examine whether spatial variation in the frequency of cell division influences tissue shape, we measured cell cycle times using dual pulse with two thymidine analogues (5-Bromo-2'-deoxyuridine/iododeoxyuridine (BrdU/IdU)) 54 . Each of the epithelial and mesenchymal tissue layers were arbitrarily divided into twelve spatial regions within which mean cell cycle times were calculated (Fig. 1B, Supplementary Fig.   1A). Cell division was most rapid in the proximal third of the mandibular arch adjacent to the face but there was little difference between the middle and distal thirds (Fig. 1C, D), implying this parameter does not intuitively explain differences in waist/bulbous morphology.
Physical tissue properties profoundly influence morphogenesis. Using atomic force microscopy (AFM) to measure elasticity (Fig. 1E, Supplementary Fig. 1B), we performed shallow (1 µm) indentation of the ~12 µm thick epithelium to exclude substrate effects of the underlying mesenchyme ( Supplementary Fig. 1C) and found that waist epithelium becomes stiffer relative to more proximal and distal flanking regions between somite stages 19 and 21 (Fig. 1F). Mesenchymal stiffness was measured using deep (7-9 µm) indentation ( Supplementary Fig. 1D) and decoupled from the influence of the epithelium (see Methods). In contrast to the epithelium, mesenchyme was least stiff in the middle region (Fig. 1F). Under shallow indentation, the arch tissue behaved as an elastic material ( Supplementary Fig. 1C), whereas deep probe indentation and retraction revealed evidence of hysteresis, or dissipation of energy, an indication of viscoelasticity ( Supplementary Fig. 1D). Combined (epithelial and mesenchymal) tissue viscosity that was quantified using different rates (5, 10, and 15 µm/s) of indentation ( Supplementary Fig. 1E) also increased over developmental time but did not vary spatially throughout the arch (Fig. 1G). An unbiased model would be useful to evaluate the potential morphogenetic relevance of these data.
To integrate the influence of cell divisions and physical properties on tissue shape, we constructed a 3D, two tissue layer finite element model of the 19 somite 6 stage mandibular arch that was based on OPT-derived tissue topography ( Supplementary Fig. 1F, G), an approach conceptually similar to that previously reported for limb bud shape 30 but with the addition of empirical physical properties.
Based on prior work, we initially hypothesised that disproportionately increased stiffness of the middle epithelium might resist hoop stress due to growth of the mesenchyme to yield a growth process reminiscent of directed dilation 55,56 . However, simulated deformation predicted an inappropriately short and wide arch (Fig. 1H, Supplementary Mov. 3). We reasoned that the inadequacy of this continuum model might reflect the fact that it did not account for defined cell rearrangements.

Distinct cellular parameters characterise two regions of the mandibular arch
In confluent 2D epithelia, defined neighbour exchange processes are essential for tissue remodelling. We noticed that the mesenchymal cells within the mandibular arch exhibited key characteristics of mouse epithelial cells that rearrange through neighbour exchange, such as confluence, abundant expression of cell-cell junction proteins (N-cadherin and desmoglein), and protrusive activity (Supplementary Fig. 2A- 14,57 . Since biological parameters that are relevant to the possibility of 3D cell intercalation have not been well defined, we explored ideas from the physical sciences that are hypothetically relevant to morphogenesis. We performed live lightsheet microscopy of intact mouse embryos by combining transgenic CAG::H2B-GFP and mTmG reporters to highlight nuclei in green and cell membranes in red (Supplementary Mov. 4,5). As in an unstable foam 58,59 , mesenchymal cells exhibited a broad distribution of cell faces (7)(8)(9)(10)(11)(12)(13)(14) with relatively few neighbours in the mid-portion of the mandibular arch ( Fig. 2A,B, Supplementary Fig. 2D, Supplementary Mov. 6), suggesting cells in that region are furthest from equilibrium and most likely to exchange neighbours.
To estimate cell shapes, we segmented nuclei in 3D to act as centroids for Voronoi tessellation (Fig. 2C). According to a recent model, there is a relationship between the rigidity of confluent 3D tissues and the ratio of cellular surface area to volume 60 . The cell shape parameter surface area/volume 2/3 (S/V 2/3 ) varied along the proximodistal axis of the mandibular arch with the highest values observed in the middle region (Fig. 2D, E) that is consistent with a relatively more 'liquid' behaviour compared to proximal and 7 distal regions. These parameters predict that middle region cells should preferentially engage in neighbour exchange.
To identify the large-scale pattern of tissue displacement, a subset of fluorescently labelled nuclei were tracked in 4D after accounting for embryo drift by marking multiple fluorescent beads that we co-embedded with the embryo in an agarose cylinder. Tissue growth was relatively longitudinal in the middle region compared to the distal region (Fig. 2F an observation that can potentially be explained by convergent cell movements. To test for this possibility, we first examined epithelial cells at higher resolution using live confocal time-lapse imaging. In the middle epithelium, although the alignment of daughter cells was biased along the short rostrocaudal axis, T1 exchange events tended to shorten the rostrocaudal axis and elongate the proximodistal axis of growth. Cell rearrangements were less oriented in the distal region (Fig. 3A revealed that cells in the middle region converged centripetally relative to one another as tissue growed longitudinally (Fig. 3C, Supplementary Mov. 12). At small scales (~10 cells), the intercalation of a single cell into a nest of 5-6 others was the smallest multicellular unit in which 3D neighbour exchange was observed (Fig. 3C, Supplementary Mov. [13][14][15]. This configuration is analogous to 3D T1 exchange in an unstable foam 59 . Tracking of nuclear centroids undergoing intercalation confirmed that 8 small groups of cells converged in the axial plane as the tissue extended distalward ( Supplementary Fig. 3B). In contrast, more subtle intercellular adjustments characterised the distal region (Fig. 3C, Supplementary Fig. 3C, Supplementary Mov. 16). These observations support the concept that regional differences in cell intercalation correlate with large-scale growth patterns and that volumetric convergent extension elongates the middle region (Fig. 3D).
Cortical actomyosin can orient forces that drive cell intercalation in epithelia and in mesoderm 26,63,64 . F-actin and phospho (p)-myosin light chain (pMLC) were biased parallel to the short, transverse axis among epithelial and mesenchymal cells in the middle waist, but not proximal and distal regions, of the arch (Fig. 3E, Supplementary   Fig. 3D). This bias likely reflects the tissue stress pattern 14 and is consistent with the axis of intercellular movements observed in the waist region, but itself does not explain why cells intercalate.

Oscillatory amplitude of cortical tension correlates with mesenchymal cell intercalation
Cortical tension is a key parameter that regulates cell sorting and intercalation during development [65][66][67] . Local actomyosin abundance or cell interface length observations have been used as a proxy for cortical tension, but may not reflect either actual forces or their dynamic fluctuations. To directly measure cortical tension, we knocked-in a conditional FRET (Förster resonance energy transfer)-based vinculin tension sensor (VinTS), for which fluorescence lifetime in nanoseconds (ns) is proportional to force in piconewtons (pN) 68 , into the mouse Rosa locus. We also generated two control knock-in strains that should exhibit maximal (donor only VinTFPno FRET), and minimal (vinculin tailless VinTL -maximal FRET) fluorescence lifetime, respectively (Fig. 4A).
All three knock-in constructs were expressed robustly in the appropriate cortical Measurements of the dynamic range, floor and ceiling lifetime values of the three strains were undertaken in ES cell colonies and embryoid bodies prior to their evaluation in the mouse embryo under conditions that we previously optimised for live imaging 14,32 .
Single cell cortices were outlined as regions of interest to measure lifetime. As expected, the donor-only VinTFP construct reported the longest lifetime with a narrow 9 standard deviation and VinTL exhibited short lifetime values. In embryoid body cells and among differentiated beating cardiomyocytes, the range and standard deviation of the full length VinTS lifetime values was greater than that of either control suggesting the reporter was responding dynamically to cell contractions ( Supplementary Fig. 4B 25,26) were diminished in the mutant middle arch. Together, these data imply that Wnt5a acts through the cell polarity and Ca 2+ pathways to promote and orient cell intercalations.
The Wnt5a expression domain is biased distally and diminishes steeply within the middle region of the arch, but it was not clear whether it acts instructively or permissively to influence cortical behaviour. To test between these possibilities, we overexpressed a transgenic Cre-activated Wnt5a allele that was targeted to the  Supplementary Fig. 7A), implying that the native Wnt5a expression domain provides a spatial cue for cortical organisation.
We examined the Hippo pathway since it has been implicated in craniofacial malformation 57,58 , is mechanoresponsive 71,72 , and is a downstream effector of noncanonical WNT5A signalling that promotes YAP/TAZ nuclear accumulation 73 . In To further test whether cytosolic Ca 2+ transients contribute to mandibular arch morphogenesis using another genetic perturbation, we examined Piezo1 which encodes a mechanosensitive ion channel 74 . As expected, Ca 2+ fluctuation was diminished in

DISCUSSION
Our findings suggest that cell intercalations shape a volume of confluent cells, and that basic modes of 2D cell rearrangement, such as T1 exchange, have 3D counterparts previously observed in foams that remodel mesenchyme.
Step-wise evolution of cell intercalation capacity from in-plane among diploblasts 75 , to out-of-plane among triploblasts 76 , to within a volume of cell neighbours may have facilitated the radiation of increasingly complex body plans among Bilateria and vertebrates.
By acting partly in the same pathway, Wnt5a, Yap/Taz and Piezo1 transform biochemical signals to mechanical outputs that permit cell intercalation. In particular, oscillatory contractions of the cytoskeleton that have been observed in association with multiple types of invertebrate and vertebrate cell movements 9,63,77-83 are likely essential for overcoming an energy barrier for cell intercalation 23,24 . The spatial coordination of cell polarity with cortical oscillation by Wnt5a upstream of YAP/TAZ and PIEZO1 effectors ensures that cell intercalations are oriented appropriately.
Explanations for the oscillatory nature of contractions that have been put forward include cell-extrinsic [84][85][86] and cell-intrinsic mechanisms 87,88 69,89,90 , including Ca 2+ flux 70,79 . In Drosophila, ion channel function is required to drive Ca 2+ fluctuation and periodic cell contraction 70 , whereas in the mouse embryo, Piezo1 partially fulfills this function. In our system, feedback between positive and negative regulators of Ca 2+ influx, such as the noncanonical Wnt pathway and Ca 2+ -dependent proteases like calpain-2, respectively, have the potential to regulate oscillation amplitude.
Gradual stiffening of mandibular arch tissue that we observed is conceptually similar to what has been observed over the course of dorsal closure due to cell contractions in the amnioserosa of Drosophila 91 . The solidification of tissue after early morphogenetic movements establish primordial structures implies that a different suite of cell and tissue properties, possibly related to extracellular matrix and differentiating tissues, may regulate morphogenesis of solid organs at later stages. Combining increasingly accurate biophysical approaches with genetics will likely help to define morphogenesis pathways, including those that coordinate cell polarity with physical properties.
Vinculin tension sensor knock-in mouse strains To target the Rosa26 locus, constructs were cloned using the following plasmids: vinculin tension sensor (VinTS) and vinculin tailless (VinTL) 68 (Addgene plasmid#: 26019, 260020), and Ai27 (gift from Hongkui Zeng 96 ; Addgene plasmid#: 34630). To generate VinTS targeting vector, Mlu1 sites were introduced upstream of the start codon and downstream of the stop codon in VinTS using PCR. To generate VinTL, an Mlu1 site was introduced upstream of the start codon and a stop codon followed by an Mlu1 site downstream of the Venus sequence. To generate vinculin teal fluorescent protein (VinTFP -FRET donor only), an Mlu1 site was introduced upstream of the start codon and a stop codon followed by an Mlu1 site downstream of the mTFP1 sequence. PCR products were digested with Mlu1 and purified using Qiaex gel purification kit (Qiagen). Reverse primers for generating VinTL and VinTFP were identical, so the constructs were distinguished based on size in an agarose gel following Mlu1 digestion and gel purification and bands were cut out accordingly. The inserted construct in the Ai27 Rosa26 targeting vector was removed with Mlu1 and replaced with VinTS, VinTL, or VinTFP. Sequences for all targeting vectors were confirmed through DNA sequencing (performed by The Centre for Applied Genomics, The Hospital for Sick Children). The final targeting vectors were constructed as follows: CAG enhancer - Generation of ES cell lines and generation of chimeras were performed by the Transgenic Core at the Toronto Centre for Phenogenomics. Briefly, linearised constructs were electroporated into G4 ES cells and G418-resistent clones were screened by PCR. 4 positive clones from VinTS, and 2 positive clones from each of VinTL and VinTFP were aggregated with CD1 morula to obtain chimeric mice following standard procedures. Chimeric mice were outbred to CD1 mice to obtain an F1 generation through germline transmission. All procedures involving animals were performed in compliance with the Animals for Research Act of Ontario and the Guidelines of the Canadian Council on Animal Care. The Toronto Centre for Phenogenomics (TCP) Animal Care Committee and Hospital for Sick Children Animal Care Committee reviewed and approved all procedures conducted on animals at TCP and at the Hospital for Sick Children, respectively.

Z/Wnt5a conditional overexpression mouse strain
The Z/Wnt5a line was generated by targeting a Cre-activated Wnt5a expression vector to the endogenous Ubiquitin-b (Ubb) locus (unpublished reagent provided by Phil Smallwood and Jeremy Nathans). The Cre-activated Wnt5a expression vector was constructed using a similar strategy as described for generating the Z/Norrin expression cassette 97 . Expression of the Wnt5a transgene is activated only after Cremediated recombination, which removes a LacZ-STOP cassette upstream of the Wnt5a open reading frame. Sox2:Cre 98 was employed to drive ubiquitous expression.
Optical projection tomography E9.5 mouse embryos were harvested and fixed in 4% paraformaldehyde overnight at 4°C. OPT was performed using a system that was custom-built and is fully described elsewhere 99 . Three-dimensional (3D) data sets were reconstructed from autofluorescence projection images acquired over a 25 minute scan period at an isotropic voxel size of 4.5 µm. The 3D surface renderings of the OPT data were generated by MATLAB software, version R2011b (Mathworks).

Cell cycle time measurement
Pregnant females were injected first with BrdU intraperitoneally at E9.75 and then with IddU after 2.5hr. Thirty min. following the second injection, embryos were dissected in cold PBS and fixed with 4% PFA overnight at 4 °C. Whole-mount immunofluorescence of BrdU and IddU was performed 54 .

Elasticity and viscosity measurement by atomic force microscopy
Mouse embryos were incubated in 50% rat serum in DMEM on a 35 mm dish in which 2% agarose was poured around the perimeter. The mandibular arch was immobilised to the agarose with pulled glass needles pinned through the flank adjacent to mandibular arch. The arch was examined using an AFM (BioScope Catalyst, Bruker) mounted on an inverted microscope (Nikon Eclipse-Ti). AFM indentation tests were performed using a spherical tip (radius: 15 µm) at distinct locations categorised as proximal, middle and distal mandibular arch. Spherical tips were made by assembling a borosilicate glass microsphere onto a tipless AFM cantilever using epoxy glue. The cantilever spring constant was calibrated before every experiment by measuring power spectral density of thermal noise fluctuation of the unloaded cantilever.
To determine the elastic modulus of epithelium, a trigger force of 300 pN was consistently applied. For both small and large indentation measurements in each region (proximal, middle, and distal), 15 locations were measured and repeated in triplicate, amounting to 45 measurements at each region. Because the epithelial thickness is approximately 10 µm, we followed the empirical 10% rule 100 to indent epithelium up to 1 µm in depth to avoid influence from the mesenchyme. The Hertz model for a spherical tip was used to calculate the elastic modulus of the epithelium from the small indentation data. To determine mesenchymal elastic modulus and the overall tissue viscosity, we applied large indentation (depth: 7-10 µm) at indentation rates of 5, 10 and 15 µm/s. The Kelvin-Voigt model was used to fit the large indentation forcedisplacement data. To extract overall tissue viscosity, the range of data beyond 1.5 µm indentation depth was used, and the elastic range was neglected. The elastic modulus value of mesenchyme was then determined by using experimental force-displacement data and finite element simulation.

a) Determination of epithelium's elastic modulus
For small indentation, the Hertz model for a spherical tip was used to fit the experimental force-displacement data and determine epithelial elastic modulus values. The relationship between the indentation depth d and the loading force F is where , are the elastic modulus and Poisson's ratio of the indenter; and , are the elastic modulus and Poisson's ratio of epithelium. The spherical tip was made of borosilicate glass (elastic modulus and Poisson's ratio: 63 Gpa and 0.2). The Possion's ratio for epithelium was set to 0.4 101 . Using the experimental data from small indentation as well as the above calculation, epithelial elastic modulus was quantified.

b) Determination of the overall embryonic tissue viscosity
For large indentation, the Kelvin-Voigt model was used to fit experimental forcedisplacement data. Stress-strain relation in the Kelvin-Voigt model is Eq. (1) When the equation is multiplied by contact area , where a is the contact radius, the left-hand side results in total force applied to epithelium and mesenchyme. For a bilayer structure, the contact radius is a function of the first-second layer elastic mismatch ratio , the first layer thickness t, indentation depth d, indenter radius R. Comparing the elastic modulus of epithelium E epithelium and the overall modulus (i.e., epithelium and mesenchyme both included), we found the ratio E epithelium /E mesenchyme ) was small (~2). Thus, according to the Hertz model 102 , . Rewriting Eq. (1) gives Eq. (2) where v is indentation rate. It is evident that is rate-independent while is rate-dependent. Therefore, and were determined with the forcedisplacement data measured at different indentation rates, and viscosity was also calculated. Furthermore, was exported into the finite element model to calculate mesenchyme's elastic modulus.

c) Determination of mesenchyme's elastic modulus
A snapshot of the meshed 2D axisymmetric finite element model with a bilayer structure (epithelium and mesenchyme) under frictionless loading is shown in Supplementary Fig.  1B. Supplementary Fig. 1F shows the steps we used to conduct iterative FE simulation to quantify mesenchyme's elastic modulus. As in the above section, for each displacement, was determined. This elastic force applied to the overall tissue was incorporated into the finite element model. Since epithelial elastic modulus has been determined, different modulus values were assigned to the mesenchymal layer in the finite element model until finite element-obtained force-displacement curves agreed well with the experimental curves (Fig. 1F). Mesenchymal elastic modulus was saved once the R-square value (correlation coefficient between the two curves) was greater than the threshold value (0.99).

Finite element modelling
An OPT (optical projection tomography) image stack was first concatenated and reconstructed using ImageJ, and a 3D model was exported in the STL format. We used MeshLab to isolate the mandibular arch from the embryo. Quadric edge collapse decimation algorithm was employed to reduce the total number of 3D triangular mesh faces to the target number of faces (~5,000 without distorting the geometry). The model was then imported into Solidworks in which the 3D mandibular arch model was segmented into two layers (epithelium and mesenchyme) with 24 regions based on the geometric locations of cell cycle time measurements. The finite element model was fixed in all six degrees of freedom (Displacement: U x =U y =U z =0, Rotation: U Rx =U Ry =U Rz =0) at the extended proximal end to ensure the boundary condition did not influence growth of the proximal region (Supplementary Figure 1G.). A ten-node tetrahedral element (SOLID 186) was selected to discretise the model.
Each region of the model was assumed to be viscoelastic, isotropic and homogeneous. The viscoelastic property of each region was assigned with an average value obtained from experimental AFM measurement and implemented in ANSYS v15.0 (ANSYS Inc., Canonsburg, PA) with instantaneous elasticity and two-pair Prony relaxation. We also performed comparative simulation with different viscoelastic values within the range of our AFM measurement and observed no significant effect in the predicted tissue shape change.
The experimentally measured 3D cell cycle time values were converted to strain using the method described previously 30 , and strain values were incorporated in the finite element model for tissue shape prediction. Cell density was considered to be the number of cells per volume.
. Therefore, tissue volume change was a function of cell number change and cell density change. We started by assuming cell density remains constant (changes in cell density were incorporated later as a correction factor), and tissue volume change was proportional to cell number change . Volume strain induced by cell number change was thus equal to . was calculated from cell doubling time. Cell density change (measured to be 1.7 % per hour) was incorporated into volume strain as a correction factor . Hence, the overall volume strain was .
Parameters incorporated into the model: Voronoi tessellation and rigidity analysis Using light sheet microscopy, we obtained approximately 1,000 2-dimensional images (ML-PD plane) of the mandibular arch, each image about 0.4 microns apart from the next along the perpendicular RC axis. Cell nuclei marked by H2B-GFP emitted light with relatively high intensity. Each image was processed as following: a) using a Gaussian deconvolution with a standard deviation roughly the size of one cell, the images were smoothened. b) Local maxima were sought in square boxes, again, roughly the size of one cell. Each local maximum was marked as a cell centre. This process was repeated for each image in ML-PD plane. The layers of marked cells were then compared against one other. If a point was marked to be the centre of a cell within 7 or more consecutive layers in the stack, the middle layer was marked as the RC position of that cell. This process gave us a 3D representation of roughly 6,000 cell nuclei in the tissue. Voronoi tessellation was performed using these cell nuclei as nodes for the tessellation algorithm.

Live, time-lapse confocal microscopy
Live image acquisition was performed as described previously 14,32 . Briefly, embryos were submerged in 50% rat serum in DMEM without phenol red (Invitrogen) in a 25 mm imaging chamber. Cheese cloth was used to immobilise the embryo and position the mandibular arch directly against the coverglass. Embryos were imaged in a humidified chamber at 37°C in 5% CO 2 . Time-lapse images were acquired on a Quorum WaveFX-X1 spinning disk confocal system (Quorum Technologies Inc.) at 20X magnification. Images were processed with Volocity software or ImageJ/Fiji. Representative images are shown from at least 3 independent experiments for each condition, and unless otherwise indicated, from at least 3 independent cohorts. No statistical method was used to predetermine sample size. Experiments were not randomised. Investigators were not blinded to allocation during experiments and outcome assessment.

Live, time-lapse light sheet microscopy
Three-dimensional (3D) time-lapse microscopy was performed on a Zeiss Lightsheet Z.1. microscope. Embryos were suspended in a solution of DMEM without phenol red containing 12.5% rat serum and 1% low-melt agarose (Invitrogen) in a glass capillary tube. Once the agarose had solidified, the capillary was submerged into an imaging chamber containing DMEM without phenol red, and the agarose plug was partially extruded from the capillary until the portion containing the embryo was completely outside of the capillary. The temperature of the imaging chamber was maintained at 37° C with 5% CO 2 . Images were acquired using a 20X/1.0 objective with dual-side illumination, and a z-interval of 0.479 µm. All experiments were imaged in multi-view mode with 3 evenly-spaced views spanning approximately 90 degrees (from a frontal view to a sagittal view of the mandibular arch). Images were acquired for 3-4 hours with 10 minute intervals. Fluorescent beads (Fluospheres 1µm, Thermofisher, 1:10 6 ) were used as fiducial markers for 3D reconstruction and to aid in drift-correction for cell tracking. Multi-view processing was performed with Zen 2014 SP1 software to merge the 3 separate views and generate a single 3-dimensional image. Further analysis and cell tracking were performed using Arivis Vision4D software (Arivis).
Membrane segmentation and 3D cell neighbour counting 3D timelapse datasets of cell membranes were processed with the ImageJ macro 'TissueCellSegmentMovie' (kindly provided by Dr. Sébastien Tosi from the Advanced Digital Microscopy Core Facility of the IRB Barcelona) to generate membrane segments prior to analysis with Imaris software (Bitplane). Surface objects were created using Imaris and this data was used for 3D cell neighbour analysis. Cell neighbours were manually counted by identfying the target cell and counting all cells which share an interface within the plane, as well as adjacent cells in the planes above and below. Analysis was performed on 3 separate areas in both middle and distal regions of the mandibular arch over 2 independent experiments for each condition.

Cell tracking and dandelion plots
Cell tracks (cell positions tracked over time) were calculated manually. Cell nuclei were followed between z-stacks of images as described above, each z-stack separated from the next by 5 or 10 minutes. The large drift between images over time and the resolution of the images made it difficult to follow more than 130 cells throughout the entire movie. Only cells that could reliably be identified and followed by eye in at least 33 frames were considered for the random walk analysis.
For each movie, the z-stacks for each time point were aligned, and 'fusion' stacks were created to generate z-plane images based on the mean voxel intensity at each voxel. The 'fused' stacks were then imported into Arivis Vision 4D software (arivis AG, Unterschleißheim, Germany), and automated tracking was used to generate cell tracks. Tracks were validated manually, and validity annotations were entered into an Excel spreadsheet. Tracks were defined to be valid at a given timepoint if the segment determining the track's location at that timepoint was centred in the middle of a nucleus. Tracks were defined to be suitable for use in further analysis if time between their first valid timepoint and final valid timepoint was 150 minutes or greater. Whether a track tracked an epithelial or mesenchymal cell was determined observing the nuclear location of the track relative to the tissue boundary as well as the morphology of the nucleus (epithelial cells tended to have more elongated, columnar shapes relative to their counterparts in the mesenchyme).
To correct for drift, the frame by frame displacement of red fluorescent beads that were embedded adjacent to the embryo within the agarose plug used in the light sheet microscope was calculated. These displacements were imported into MATLAB for initial track concatenation and drift correction. Track and segment information and validity were acquired on Arivis. The concatenation function returned drift corrected tracks that were filtered to only include valid tracks. Tracks could then be plotted, and end to end displacements calculated and plotted.

Random walk model
We described cell motions from tracking experiments by stochastic processes. In particular, we adopted the Ornstein-Uhlenbeck (OU) process 103 for our analysis. In an OU-process, the trajectory of a particle is determined by a relation describing its change in velocity over time. The change of velocity in the model is proportional to its velocity in the past (persistent) plus a randomly generated term (random walk). This approach has been used to analyse the properties of cell migrations under many contexts including tumour growth 62 and wound repair 61 .
The OU-process is defined by the Langevin equation

Xiao Xiao
July 13,2016 The stochastic process his section, we describe cell motions from tracking experiments by stochastic processes. In icular, we adopt the Ornstein-Uhlenbeck (OU) process (Uhlenbeck and Ornstein, 1931) for our lysis. The OU-process has been used to analyze the properties of cell migrations under many exts including tumor growth (Wu et al., 2014) and wound repair .
The OU-process is defined by the Langevin equation re v is the cell velocity, t is time, D is the di↵usion coe cient, vector w describes a Wiener ess, and ⌧ is the time scale often referred as the persistent time. The persistent time, which be understood as the length of time a given velocity "remembers" itself, describes the time of velocity auto-correlation function (1) where v is the cell velocity, t is time, D is the diffusion coefficient, vector w describes a Wiener process, and the bottom left of Fig. 1. ing Wu et al. (2014), we simulate cell trajectories by applying first-order Euler's scheme n (1) to obtain ⇠ N (0, 1) and S is the cell speed with D = S 2 ⌧ . We apply principle component analysis ed cell trajectories prior to our analysis so that we can simulate cell displacement in tion separately. In other words, we diagonalize the correlation coe cient matrix so that al components are zero.
mulated trajectories and MSDs are in Fig. 2. For both wild type and mutant scenarios, (4) systematically underestimate the mean squared displacements for a given time lag. epancy could come from the fact that we ignored the correlations between neighboring e that, for the wild type tissue, there is a narrow middle region and a wider distal region. ore further compare the persistent time (of the first principle direction), ⌧ , and volatility etween middle and distal regions. Fig. 3 shows larger ⌧ with standard deviation smaller dle region than that in the distal region (with p-value less than 0.01), while there is less in terms of volatility. 3 is the time scale often referred to as the persistent time. The persistent time, which may be understood as the length of time a given velocity "remembers" itself, describes the time of the velocity auto-correlation function he OU-process is defined by the Langevin equation re v is the cell velocity, t is time, D is the di↵usion coe cient, vector w describes a Wien ess, and ⌧ is the time scale often referred as the persistent time. The persistent time, whi be understood as the length of time a given velocity "remembers" itself, describes the time velocity auto-correlation function re n is the space dimension of the tracks. The mean squared displacement (MSD) is given b (2) and (3) will be used to fit the observed cell tracks to obtain the persistent time ⌧ an i↵usivity coe cient D. Consequently, we will be able to simulate cell trajectories by equatio o further understand similarities and discrepancies between the statistics from the observatio the OU-process.
Data Analysis re we apply OU-process to describe cell motions, we first present the experimental data from omite wild type embryo and a 21 somite mutant embryo. Fig. 1a and 1b show cell trajectori the wild type and mutant embryos respectively. The Wnt5a mutant tissue exhibits ve rent shape compare to the wild type tissue. In addition, comparison of their MSDs from Fi ows that the average distance traveled by mutant cells is in general larger than that travele ild type cell for any given time lag. Further, from Fig. 1d, the auto-correlation of veloci the mutant tissue has a slower decrease at long time scale (40 min) compare to the wild typ e. 1 (2) where n is the space dimension of the tracks. The mean squared displacement (MSD) is given by ts including tumor growth (Wu et al., 2014) and wound repair ). e OU-process is defined by the Langevin equation v is the cell velocity, t is time, D is the di↵usion coe cient, vector w describes a Wie s, and ⌧ is the time scale often referred as the persistent time. The persistent time, wh e understood as the length of time a given velocity "remembers" itself, describes the time ocity auto-correlation function n is the space dimension of the tracks. The mean squared displacement (MSD) is given on (2) and (3) will be used to fit the observed cell tracks to obtain the persistent time ⌧ a usivity coe cient D. Consequently, we will be able to simulate cell trajectories by equat further understand similarities and discrepancies between the statistics from the observati e OU-process.
ata Analysis we apply OU-process to describe cell motions, we first present the experimental data from ite wild type embryo and a 21 somite mutant embryo. Fig. 1a and 1b show cell trajector he wild type and mutant embryos respectively. The Wnt5a mutant tissue exhibits v nt shape compare to the wild type tissue. In addition, comparison of their MSDs from F ws that the average distance traveled by mutant cells is in general larger than that trave d type cell for any given time lag. Further, from Fig. 1d, the auto-correlation of veloc he mutant tissue has a slower decrease at long time scale (40 min) compare to the wild ty 1 Equation (2) and (3) was used to fit the observed cell tracks to obtain the persistent time ed for the numerical simulation contains n = 179 number of cells interval of t = 5 min over a 3-hour's duration. The cell trajectories Fig. 1 from mid (red) to distal (blue) regions, and the MSD is shown Fig. 1. ), we simulate cell trajectories by applying first-order Euler's scheme he cell speed with D = S 2 ⌧ . We apply principle component analysis prior to our analysis so that we can simulate cell displacement in ther words, we diagonalize the correlation coe cient matrix so that ero.
and MSDs are in Fig. 2. For both wild type and mutant scenarios, nderestimate the mean squared displacements for a given time lag. from the fact that we ignored the correlations between neighboring ype tissue, there is a narrow middle region and a wider distal region. the persistent time (of the first principle direction), ⌧ , and volatility istal regions. Fig. 3 shows larger ⌧ with standard deviation smaller t in the distal region (with p-value less than 0.01), while there is less y.
where W ⇠ N (0, 1) and S is the cell speed with D = S 2 ⌧ . We apply principle component analysis to observed cell trajectories prior to our analysis so that we can simulate cell displacement in each direction separately. In other words, we diagonalize the correlation coe cient matrix so that o↵-diagonal components are zero.
The simulated trajectories and MSDs are in Fig. 2. For both wild type and mutant scenarios, equation (4) systematically underestimate the mean squared displacements for a given time lag. This discrepancy could come from the fact that we ignored the correlations between neighboring cells. Note that, for the wild type tissue, there is a narrow middle region and a wider distal region. We therefore further compare the persistent time (of the first principle direction), ⌧ , and volatility p S 2 /⌧ between middle and distal regions. Fig. 3 shows larger ⌧ with standard deviation smaller in the middle region than that in the distal region (with p-value less than 0.01), while there is less di↵erence in terms of volatility.
where W ⇠ N (0, 1) and S is the cell speed with D = S 2 ⌧ . We apply principle component to observed cell trajectories prior to our analysis so that we can simulate cell displace each direction separately. In other words, we diagonalize the correlation coe cient matrix o↵-diagonal components are zero.
The simulated trajectories and MSDs are in Fig. 2. For both wild type and mutant sc equation (4) systematically underestimate the mean squared displacements for a given t This discrepancy could come from the fact that we ignored the correlations between neig cells. Note that, for the wild type tissue, there is a narrow middle region and a wider distal We therefore further compare the persistent time (of the first principle direction), ⌧ , and v p S 2 /⌧ between middle and distal regions. Fig. 3 shows larger ⌧ with standard deviation in the middle region than that in the distal region (with p-value less than 0.01), while ther di↵erence in terms of volatility. . We applied principle component analysis to observed cell trajectories prior to our analysis so that we could simulate cell displacement in each direction separately. In other words, we diagonalised the correlation coefficient matrix so that off-diagonal components were zero.
An important charcteristic of a random walk model is its mean squared distance (MSD). For an arbitrary trajectory, the MSD as a function of time follows a power-law, with power of 0 representing a truly random trajectory, and power of 2 representing movement in a straight line with no randomness. On a log-log plot, these two extremes translate into lines with slope 0, or a horizontal line, for the random trajectory, and a line of slope 2 for the walk in a straight line. A persistent random walk, however, is characterized by slope 1, the short black line in the figure. The analysis of cell trajectories (based on light sheet microscopy) suggested that mandibular arch cells exhibited a MSD slope that is characteristic of a persistent random walk.

Strain analysis
A rectangular grid of points was superimposed on the first frame of a rostrocaudalproximodistal plane of a time-lapse light sheet movie of the mandibular arch. The points were followed in subsequent frames by calculating the correlation function of a box around each point in the initial time frame to all the boxes of the same size in the vicinity of the original box in the next frame. The vector that connected the location of the box in the first frame to the location of the neighbouring box with the highest correlation with the original box in the second frame was the displacement vector. The points were moved by this displacement vector in each time frame, and this process was repeated for all 31 time frames.

Immunostaining
Embryonic day (E) 9.0-9.5 mouse embryos were fixed overnight in 4% paraformaldehyde in PBS followed by 3 washes in PBS. Embryos were permeabilised in 0.1% Triton X-100 in PBS for 20 min and blocked in 5% normal donkey serum (in 0.05% Triton X-100 in PBS) for 1h. Embryos were incubated in primary antibody overnight incubation at 4 • C. Embryos were washed in 0.05% Triton X-100 in PBS (4 washes, 20 min each), and then incubated in secondary antibody (1:1000) for 1 h at room temperature. Embryos were washed (4 washes, 20 min each), followed by a final wash overnight at 4 • C, and stored in PBS. Images were acquired using a Quorum spinning Disk confocal microscope (Zeiss) at 10 X, 20 X or 40 X magnification, and image analysis was performed using Volocity software (Perkin Elmer) and ImageJ.

Whole mount in situ hybridisation
Whole mount in situ hybridisation was performed as described 104 . Wildtype and mutant littermate embryos were processed identically in the same assay for comparison. The Wnt5a riboprobe was gift from A. P. McMahon.

Quantification of polarised actin and myosin distribution
Single confocal slices taken 2 µm above (for epithelium) and below (for mesenchyme) the basal surface of epithelial cells stained with phospho-myosin light chain 2 (Thr18/Ser19) (pMLC), rhodamine-phalloidin or Alexa Fluor 633 phalloidin were analysed using SIESTA software as described previously 14,105 . Cell interfaces were manually identified, and average fluorescence intensities were calculated for all interfaces and grouped into 15° angular bins, with 0°-15° bin representing interfaces that are parallel with the AP axis (PD interfaces) and 75°-90° bin representing interfaces that are parallel with the PD axis (AP interfaces). Average fluorescence intensity values for each bin were normalised to average fluorescence intensity of PD interfaces (0°-15° angular bin). Error bars indicate standard error of the mean and p values were calculated using Student's t-test.

Quantification of cell behaviours
Metaphase-to-telophase transition angles were measured as described 32 . Epithelial tetrad formation and resolution angles were measured by first assigning a proximodistal reference axis taken from a low 10 X confocal magnification view of the embryo flank. Tetrads were identified manually, frame by frame. The angle between the long axis of the ellipse outlined by each tetrad and the reference axis was documented at the beginning of a given movie and upon resolution.

Live, time-lapse fluorescence lifetime analyses in vitro and in vivo
Fluorescence lifetime microscopy (FLIM) was performed on a Nikon A1R Si laser scanning confocal microscope equipped with PicoHarp 300 TCSPC module and a 440 nm pulsed diode laser (Picoquant). Data were acquired with a 40 x/1.25 water immersion objective with a pixel dwell time of 12.1 µs/pixel, 512 x 512 resolution, and a repetition rate of 20 MHz. Fluorescence emission of mTFP1 was collected through a 482/35 bandpass filter. Embryos were prepared as described above for live timelapse microscopy and imaged in a humidified chamber at 37°C in 5% CO 2 . Data were acquired over 15 frames at 2 minute intervals for 20 minutes.
Fluorescence lifetime of mTFP1 was determined using n-exponential reconvolution model in SymphoTime software (Picoquant) with model parameters n=2 for VinTS and VinTL and n=1 for VinTFP. Fitting was performed to achieve a chi-squared of χ 2 =1.000 ± 0.100.

Inhibitor treatment
The effect of inhibitors Y27632 (Sigma #Y0503) and Cytochalasin D on fluorescence lifetime of VinTS were conducted as follows: Embryos were incubated with 20 µM Y27632 or 20 µg/mL Cytochalasin D for 15 minutes in 50% rat serum with DMEM in roller culture prior to experiments that were conducted using the same conditions described above.

Cytosolic calcium fluctuation
Calcium indicators Fluo-8 AM (Abcam #142773) or X-rhod-1 AM (Invitrogen #X14210) at 10 mM were added in 2 ml of 50% rat serum medium and incubated for 30 min. at 37 °C. Embryos was permiabilised with 0.1% Pluronic F-127 (Invitrogen #P3000MP) in culture medium for 20 min. before X-rhod-1 staining. The culture medium was removed and washed (2 times) and replaced with 2 ml culture medium. Live cell calcium imaging was performed on a Quorum Spinning Disk confocal microscope (Zeiss) equipped with a 40 X water objective lens or a Nikon A1 confocal microscope (Nikon) equipped with a 20 X dry objective lens. Calcium indicators were excited with an argon laser line (488 nm), and emissions were recorded in the green channel (500-560 nm) for Fluo-8 AM (acetoxyomethyl) and red channel (600-700 nm) for X-rhod-1 AM. Images were acquired every 2 or 5 min. for up to 20 min.; image and data acquisition was performed using Volocity software (Perkin Elmer). All imaging experiments were performed in duplicate.

VinTS/Ca 2+ correlation
We calculated the correlation between VinTS lifetime and Ca 2+ concentration data series with zero time-lag. In this study, we defined the percentage of X-rhod-1 AM staining area for each cell in relation to Ca 2+ concentration. Assume the first time series (force vs. time) are called x (x1, x2, x3, etc. for time points 1, 2, 3), and the second series are y (Ca 2+ concentration vs time). First we calculated the mean and standard deviation of x and y. Let us refer to the mean of x, µ x and standard deviation of x as σ x . µ y and σ y for y. N is the number of data points. We subtracted the means from each series and multiplied data points corresponding to the same time, and summed the results. The formula follows: We analysed the amplitude of normalised correlation by using MATLAB xcorr (https://www.mathworks.com/help/signal/ref/xcorr.html).
This will give us a number between -1 and 1. For values approaching 1, the two series are strongly correlated. Approaching 0, they are not correlated. Approaching -1 implies they are anti-correlated. .   Fig. 2F, G). G According to a the model that we employed (methods), mean squared displacement (MSD), a measure of the extent of random motion, was similar between observed and simulated cell tranjectories, thereby validating this model for statistical comparison between different regions of the arch. H Cells in the middle waist region exhibited a greater slope for cumulative distribution function (CDF) of persistent time compared to those in the distal bulbous region (p<0.01), implying motion of waist cells is more consistent over time compared to those of the bulbous region.

Movie 1
Rendering of 3D OPT image of the right mandibular arch of a 19 somite stage WT embryo.

Movie 2
Rendering of 3D OPT image of the right mandibular arch of a 21 somite stage WT embryo.

Movie 3
Rendering of 3D OPT image of the predicted shape of the right mandibular arch of a 21 somite embryo based on our finite element model. Four hours of growth (between 19-21 somite stages) were simulated starting with the shape of the actual WT 19 somite stage arch. Inputs included spatial distributions of cell cycle time, epithelial and mesenchymal Young's modulus, and whole tissue viscosity.

Movie 4
Three dimensional rendering of the right mandibular arch of a 20 somite CAG::H2B-GFP embryo imaged by live light sheet microscopy. Nuclei in the narrow mid-portion were oriented with their long axes perpendicular to the distalward axis of growth.

Movie 5
Cell membranes have been segmented in this 3D rendering of the surface epithelium together with a partial volume of the underlying mesenchyme in a 20 somite embryo harbouring the mTmG transgene for membranes and CAG::H2B-GFP for nuclei. Time lapse light sheet microscopy of the intact embryo was performed. Distal is to the lower left.

Movie 6
The neighbours of one mesenchymal cell (blue) have been coloured to facilitate counting.

Movie 7
Three dimensional trajectories of a subset of nuclei labelled with H2B-GFP in a 20 somite WT embryo. Colour coding corresponds to plot in Mov. 8.

Movie 8
Three dimensional start point-to-end point displacements (dandelion plot) of cells labelled in Mov. 7 with corresponding colour code. Red/orange cells representing the Live, time-lapse, colour-coded fluorescence lifetime evaluation of vinculin tension sensor (VinTS) among epithelial cells in the mandibular arch of an intact mouse embryo.

Movie 18
Cytosolic fluorescence intensity of the X-rhod-1 calcium indicator fluctuated asynchronously among cells in the middle region of the WT mandibular arch (see Fig.  4F, Supplementary Fig. 4G for quantification).
Movie 19 X-rhod-1 calcium indicator fluctuation among cells in the distal region of the WT mandibular arch (see Fig. 4F, Supplementary Fig. 4G for quantification).

Movie 20
Rendering of 3D OPT image of the right mandibular arch of a 19 somite stage Wnt5a -/mutant.

Movie 21
Rendering of 3D OPT image of the right mandibular arch of a 21 somite stage Wnt5a -/mutant.

Movie 22
Rendering of 3D OPT image of the predicted shape of the right mandibular arch of a 21 somite Wnt5a -/mutant based on our finite element model. Four hours of growth (between 19-21 somite stages) were simulated starting with the actual shape of the 19 somite stage arch of a Wnt5a -/mutant. Inputs included spatial distributions of cell cycle time, epithelial and mesenchymal Young's modulus, and whole tissue viscosity.

Movie 23
Three dimensional rendering of the right mandibular arch of a 20 somite CAG::H2B-GFP;Wnt5a -/embryo imaged by live light sheet microscopy. Nuclei in the middle region lacked longitudinal orientation as in the WT arch (Mov. 4).

Movie 24
A small-scale volume of several cells from within the middle region of the mandibular arch of a 20 somite CAG::H2B-GFP;Wnt5a -/embryo. The predominant view is sagittal and distal is down and to the right. Nuclei subtly adjusted positions relative to one another but did not intercalate.

Movie 25
Cytosolic fluorescence intensity of the Fluo-8 calcium indicator fluctuated among cells in the middle region of the WT mandibular arch (see Fig. 5E, Supplementary Fig. 5D for quantification).

Movie 26
Fluctuation of the cytosolic fluorescence intensity of the Fluo-8 calcium indicator was dampened among cells in the middle region of the Wnt5a -/mutant mandibular arch (see Fig. 5E, Supplementary Fig. 5D for quantification).

Movie 27
Rendering of 3D OPT image of the right mandibular arch of a 21 somite stage transgenic Sox9:Cre;Z/Wnt5a embryo that ubiquitously overexpressed Wnt5a.

Movie 28
Mesenchymal cell movements in a 21 somite T:Cre;Yap f/+ ;Taz f/f mutant mandibular arch. Intercellular movements are abundant but disoriented and not purely centripetal (compare with Mov. 12). Rostral (anterior) is toward to the top and distal is toward the right.

Movie 29
Fluctuation of the cytosolic fluorescence intensity of the Fluo-8 calcium indicator was dampened among cells in the middle region of the Piezo1 -/mutant mandibular arch (see Supplementary Fig. 7A for quantification).

Movie 30
Rendering of 3D OPT image of the right mandibular arch of a 21 somite stage Piezo1 -/mutant.          Obtain F-D curve    Lifetime range (max.