Abstract
Animal morphogenesis arises from the complex interplay between multiple mechanical and biochemical processes with mutual feedback. Developing an effective, coarse-grained description of morphogenesis is essential for understanding how these processes are coordinated across scales to form robust, functional outcomes. Here we show that the nematic order of the supracellular actin fibres in regenerating Hydra defines a slowly varying field, whose dynamics provide an effective description of the morphogenesis process. We show that topological defects in this field, which are long-lived yet display rich dynamics, act as organization centres with morphological features developing at defect sites. These observations suggest that the nematic orientation field can be considered a ‘mechanical morphogen’ whose dynamics, in conjugation with various biochemical and mechanical signalling processes, result in the robust emergence of functional patterns during morphogenesis.
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Data availability
Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
Code availability
The image analysis algorithms for layer analysis, generating projection images and extracting the actin fibre orientation are described in the Methods and are available from the corresponding author upon reasonable request.
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Acknowledgements
We thank G. Ben Yoseph for technical assistance; N. Dahan from the LS&E Imaging and Microscopy Unit for help with confocal and light-sheet microscopy; B. Hobmayer for providing transgenic Hydra expressing lifeact-GFP; V. Vitelli, C. Marchetti and J. Yeomans for discussions; N. Dye and M. Driscoll for advice on image analysis; and P. Silberzan, A. Mogilner, J. Prost, N. Dye, Y. Kafri, T. Schultheiss, G. Bunin, A. Frishman and N. Ierushalmi for comments on the manuscript. This work was supported by a grant from the European Research Council (ERC-2018-COG grant number 819174) to K.K., a grant from the Israel Science Foundation (grant number 228/17) to E.B. and a Miriam and Aaron Gutwirth Memorial Fellowship to Y.M.-S.
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Y.M.-S., E.B. and K.K. designed the experiments. Y.M.-S., L.G., L.S.-Z., A.L. and K.K. performed the experiments. Y.M.-S., L.G. and K.K. analysed the data. Y.M.-S., E.B. and K.K. wrote the paper. All co-authors discussed the results and commented on the manuscript.
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Peer review information Nature Physics thanks Benoit Ladoux and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Extended data
Extended Data Fig. 1 The structure of a mature Hydra.
a, Schematic illustration of a mature Hydra showing the organization of the supracellular actin fibers in the outer ectoderm layer (green) and in the inner endoderm layer (purple). b, Images of the ectodermal (top) and endodermal (bottom) supracellular actin fibers in the body of transgenic Hydra expressing lifeact-GFP in the ectoderm or the endoderm, respectively. The fibers in the ectoderm are aligned along the animal axis, whereas the fibers in the endoderm are aligned in a perpendicular, circumferential orientation. We focus in this work on the more prominent ectodermal fibers, which are thicker and appear continuous over supracellular scales. c, Image showing the supracellular ectodermal actin fiber organization in a small mature Hydra expressing lifeact-GFP. d, Schematic illustration of a perpendicular cross-section of the tubular Hydra body. Part of the ring cross-section is shown, depicting the external ectoderm cell layer, the internal endoderm cell layer, and the extra-cellular matrix (mesoglea) sandwiched between the two layers. The cells in each layer form a polarized epithelial sheet, with their basal surfaces facing the mesoglea, and their apical surfaces facing either the external medium in the ectoderm, or the internal gastric cavity in the endoderm. The ectodermal and endodermal arrays of supracellular fibers lie along the basal layer of each epithelial sheet, on a pair of nearly parallel 2D curved surfaces.
Extended Data Fig. 2 The director field describing the actin fibers in Hydra is slowly-varying in space and time.
Images from a time-lapse movie of a regenerating tissue fragment expressing lifeact-GFP showing the actin fiber organization at the basal surface of the ectoderm (left) together with the cortical actin at the apical surface of the ectoderm (right). The associated director field (left) and cell outlines (right) extracted from the corresponding zoomed images are also shown (bottom right panels). Three labeled cells are highlighted to illustrate the changes in cell shape over this time interval (2 min). The director field describing the actin fiber orientation varies slowly in space, with typical radii of curvature which are of the order of the tissue size and much larger than the scale of individual cells. Furthermore, while the tissue morphology and cellular shapes change considerably between the two images separated by a time interval of 2 minutes, the nematic orientation field remains stable and changes over much longer time scales (hours).
Extended Data Fig. 3 Topological defects in multi-axis Hydra.
a, Schematic illustration of the configuration of topological defects in a multi-axis Hydra that has two heads and a foot. The two heads and the foot each have a +1 defect at their tip, whereas the junction between the two axes has two −1/2 defects (one visible; the second −1/2 defect is on the opposite side). b,c, Images of a two-headed transgenic Hydra expressing lifeact-GFP in the ectoderm. b, Bright-field (left) and spinning-disk confocal (right) images showing the entire Hydra body with two heads and a foot. The arrow indicates the junction between the two body axes. c, Zoomed images showing the actin fiber organization near the junction. Left: Projected spinning-disk confocal images showing the actin fibers. Right: Images of the actin fiber orientation extracted from the image intensity gradients (black lines) and the local order parameter (color; see Methods). The −1/2 defect at the junction is clearly evident.
Extended Data Fig. 4 Topological defects in the endoderm layer in Hydra.
a, Image showing the nematic actin fiber organization in the endoderm of a small mature Hydra. The fibers are oriented in a circumferential orientation along the body axis of the animal, perpendicular to the ectodermal fibers shown in the main text (Fig. 1). b, Schematic illustration of the nematic actin fiber organization in the endoderm of a mature Hydra. The topological defects in the nematic organization of the endodermal fibers coincide with the defects in the ectodermal fibers, localized at the mouth (+1), foot (+1) and tentacles (+1 at the tip, and two −1/2 at the base). c–e, Images of the endodermal actin fiber organization containing topological defects localized at the functional morphological features of a mature Hydra: the base of the foot (c), the tip of a tentacle (d), and the tip of the mouth (e). A zoomed image (top left) and map (top right) in (e) show the vortex-like arrangement of actin fibers around the mouth. The map depicts the fiber orientations extracted from the image intensity gradients (black lines) and the local order parameter (color; see Methods). f–h, Images showing the different types of topological defects found in the endoderm of regenerating Hydra tissue spheroids: +1 defect (f), −1/2 defect (g) and +1/2 defect (h). Insets: zoomed images (left) and maps (right) of the corresponding actin fiber orientation and the local order parameter. All images shown are 2D projections extracted from 3D spinning-disk confocal z-stacks of transgenic Hydra expressing lifeact-GFP in the endoderm.
Extended Data Fig. 5 Induction of nematic order in a regenerating tissue.
a, Image of the actin fiber organization in a tissue fragment immediately after excision. The excised fragment is characterized by an open boundary and a complete nematic array of actin fibers inherited from the parent animal. b, Images from a time-lapse movie of a regenerating tissue spheroid that contains a region labeled by uncaging a photoactivatable dye (Methods). The photoactivated dye is retained within the cells in the uncaged region, allowing us to track this region over time. The ectodermal actin organization (green) and photoactivated tissue label (magenta) are shown at two time points from the movie. c, Zoomed images showing the actin organization (top) and the photoactivated dye (bottom) around the uncaged region at different time points. Initially, the actin in the folded tissue spheroid exhibits partial nematic order, with a large disordered region around the uncaged region (left). Over time, parallel actin fibers emerge in the disordered region, with an orientation that is aligned with existing fibers in the surrounding tissue. Since the fiber orientation of the surrounding regions is not uniform, localized topological defects appear in the previously disordered region (right). The image sequence depicts steps in this process, as the labeled tissue region transitions from a disordered state to an ordered one, disrupted by localized point defects. All images shown are 2D projections extracted from 3D spinning-disk confocal z-stacks of transgenic Hydra expressing lifeact-GFP in the ectoderm.
Extended Data Fig. 6 Nematic actin organization in regeneration from excised open rings.
a, Schematic illustration of an excised open tissue ring. The excised tissue ring (which contains an ordered array of fibers) is cut open along the original body axis. We have previously shown that excised open rings fold in an asymmetrical fashion into a closed spheroid6. b, The average number of localized point defects of each type (+1, −1/2 and +1/2) at different stages of open ring regeneration (shaded region – standard deviation). The configuration of point defects develops over time. c, The net charge of localized point defects as a function of time in regenerating open rings. As in regeneration from excised fragments (Fig. 2d), the net charge typically reaches +2 (the topologically required value) only at ~24 hours, after the ordered regions expand and defects become localized. The defect distribution in (b,c) was determined for a population of regenerating open rings that were imaged using a spinning-disk confocal microscope from 4 directions within square tubes at the specified time-points (T = 0, 6, 24, 48, 72 hr with N = 36, 25, 26, 27, 34 samples at each time point, respectively; see Methods). The data refers to defects that arise from the disordered regions and their evolution, and does not account for the additional defects associated with tentacle formation. d, Images from a time-lapse spinning-disk confocal movie of a regenerating open ring. An early −1/2 defect is visible at T = 18 hr. The −1/2 defect is retained and appears at the junction between the two body axes of the regenerated Hydra that has two feet and a head (T = 50 hr).
Extended Data Fig. 7 De novo formation of topological defects during Hydra regeneration.
a, Schematics of de novo defect formation: a +1 defect appears together with two −1/2 defects simultaneously with the formation of a local protrusion during tentacle formation. The +1 defect localizes to the region of highest positive curvature at the tip of the protrusion, whereas the two −1/2 defects localize at saddle regions of negative curvature at the base of the protrusion. The new tentacle emerges near an existing +1 defect that will become the site of the mouth in the regenerated animal. b, Images from a time-lapse movie showing the ectodermal actin organization during the formation of a tentacle near an existing +1 defect that will become the site of the mouth of the regenerated Hydra. The process involves the appearance of a +1 defect at the tip of an emerging protrusion together with two −1/2 defects at opposite sides of its base, which subsequently elongates to become a tentacle in the regenerated animal. 2D projection images extracted from 3D spinning-disk confocal z-stacks of a transgenic Hydra expressing lifeact-GFP in the ectoderm at different time points during this process are shown. Top right: zoomed image of the protrusion showing the actin fiber orientation extracted from the image intensity gradients (black lines) and the local order parameter (color; see Methods). The +1 defect at the tip of the protrusion and the −1/2 defect on the visible side of its base are apparent.
Extended Data Fig. 8 Hole formation in a disordered region prior to the appearance of a +1 defect.
Images from a time-lapse movie of a regenerating fragment that was incubated with fluorescent beads (Methods). Some of the beads adhere to the tissue providing labeled landmarks on the regenerating tissue. 2D projection images extracted from 3D spinning-disk confocal z-stacks of the ectodermal lifeact-GFP (green) and the beads (magenta) are shown. Images show the sample before (at 7:05 hr:min), during (7:15), and after (7:45) the formation of a hole in a disordered region that is surrounded by regions with ordered fibers that generate a very spread-out +1 defect. The beads that were trapped in the internal cavity during folding and were ejected from the hole during its rupture are visible. After several hours (10:30), following the induction of order in the region surrounding the rupture site, a localized +1 point defect develops at that site.
Supplementary information
Supplementary Video 1
Light-sheet video of a regenerating fragment. Time-lapse light-sheet video showing projected images of lifeact-GFP in a regenerating tissue fragment (top) and the corresponding nematic orientation field and local order parameter (bottom; Fig. 2b). Images are shown from four different views, each rotated by a 90° angle, as indicated. The video shows the regeneration process beginning at the early tissue spheroid stage, with regions of well-aligned fibres inherited from the original Hydra tissue as well as disordered regions. Over the first 24 h, the disordered regions become aligned through induction of order from neighbouring ordered regions, and point defects in the nematic order develop in the previously disordered regions. The evolution of the defects can be followed to the formation of the mouth and foot defining the body axis of the regenerated animal, in addition to the later formation of tentacles. The tissue dynamics characteristic of the regeneration process, including contractions, expansions and changes in shape, are apparent. The tissue outlines are indicated with dashed lines. The images were centred to correct for movements of the whole tissue. The elapsed time from excision is displayed in hours, and the scale bar is 100 µm. The horizontal streaking of the fluorescent signal apparent in some frames is an artefact of the light-sheet illumination.
Supplementary Video 2
Movement of a +1/2 defect relative to the underlying tissue. Time-lapse, spinning-disk confocal video depicting the movement of a +1/2 defect relative to the underlying tissue (Fig. 3a). The +1/2 defect moves away from the labelled tissue in the direction of its rounded end. Right: images of the lifeact-GFP signal (grey scale) overlaid with the fluorescent tissue label (green). Left: corresponding nematic orientation field and local order parameter. The defect position (cyan arrow) and labelled landmark (green arrow) are indicated. The tissue outlines are indicated with dashed lines. The images were centred and rotated to correct for movements of the whole tissue. The elapsed time from excision is displayed in hours, and the scale bar is 100 µm.
Supplementary Video 3
Annihilation of a +1/2 and a −1/2 defect. Time-lapse, spinning-disk confocal video showing the annihilation of a +1/2 and a −1/2 defect (Fig. 3d). Near the end of the video, the two defects (that have a net charge of 0) merge and the region becomes ordered with well-aligned parallel fibres. Right: images of the lifeact-GFP signal. Left: corresponding nematic orientation field and local order parameter. The position of the +1/2 and −1/2 defects are indicated (cyan and magenta arrows, respectively). The tissue outlines are indicated with dashed lines. The images were centred and rotated to correct for movements of the whole tissue. The elapsed time from excision is displayed in hours, and the scale bar is 100 µm.
Supplementary Video 4
A stationary +1 defect becomes the site of mouth formation. Time-lapse, spinning-disk confocal video showing a +1 defect that remains stationary with respect to the underlying tissue. The defect site can be followed through time and coincides with the site of head formation in the regenerated Hydra (Fig. 4a). The labelled cells located near the centre of the +1 defect can be followed directly to the mouth in the regenerated animal. Right: images of the lifeact-GFP signal (grey scale) overlaid with the fluorescent tissue label (green). Left: corresponding nematic orientation field and local order parameter. The defect position (box) and labelled landmark (green arrow) are indicated. The tissue outlines are indicated with dashed lines. The images were centred to correct for movements of the whole tissue. The elapsed time from excision is displayed in hours, and the scale bar is 100 µm.
Supplementary Video 5
The region between two +1/2 defects becomes the site of foot formation. Time-lapse, spinning-disk confocal video showing two +1/2 defects with their rounded ends facing each other moving closer together. The labelled cells located between the two +1/2 defects remain centred between the defects as they move closer, and the regenerated foot forms at this site (Fig. 4b). In this case, the final merging of the two +1/2 defects into a +1 defect at the foot occurs late in the regeneration, after the establishment of the body axis. Right: images of the lifeact-GFP signal (grey scale) overlaid with the fluorescent tissue label (green). Left: corresponding nematic orientation field and local order parameter. The defect positions (cyan arrows) and labelled landmark (green arrow) are indicated when present on the visible side of the tissue. The tissue outlines are indicated with dashed lines. The images were centred to correct for movements of the whole tissue. The elapsed time from excision is displayed in hours, and the scale bar is 100 µm.
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Source data for Fig. 2c,d.
Source Data Fig. 3
Source data for Fig. 3b.
Source Data Fig. 4
Source data for Fig. 4d,e,f.
Source Data Extended Data Fig. 6
Source data for Extended Data Fig. 6b,c.
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Maroudas-Sacks, Y., Garion, L., Shani-Zerbib, L. et al. Topological defects in the nematic order of actin fibres as organization centres of Hydra morphogenesis. Nat. Phys. 17, 251–259 (2021). https://doi.org/10.1038/s41567-020-01083-1
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DOI: https://doi.org/10.1038/s41567-020-01083-1
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