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Mechanical heterogeneity along single cell-cell junctions is driven by lateral clustering of cadherins during vertebrate axis elongation

  1. Robert J Huebner
  2. Abdul Naseer Malmi-Kakkada
  3. Sena Sarıkaya
  4. Shinuo Weng
  5. D Thirumalai  Is a corresponding author
  6. John B Wallingford  Is a corresponding author
  1. Department of Molecular Biosciences, University of Texas, United States
  2. Department of Chemistry, University of Texas, United States
  3. Department of Chemistry and Physics, Augusta University, Georgia
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Cite this article as: eLife 2021;10:e65390 doi: 10.7554/eLife.65390

Abstract

Morphogenesis is governed by the interplay of molecular signals and mechanical forces across multiple length scales. The last decade has seen tremendous advances in our understanding of the dynamics of protein localization and turnover at subcellular length scales, and at the other end of the spectrum, of mechanics at tissue-level length scales. Integrating the two remains a challenge, however, because we lack a detailed understanding of the subcellular patterns of mechanical properties of cells within tissues. Here, in the context of the elongating body axis of Xenopus embryos, we combine tools from cell biology and physics to demonstrate that individual cell-cell junctions display finely-patterned local mechanical heterogeneity along their length. We show that such local mechanical patterning is essential for the cell movements of convergent extension and is imparted by locally patterned clustering of a classical cadherin. Finally, the patterning of cadherins and thus local mechanics along cell-cell junctions are controlled by Planar Cell Polarity signaling, a key genetic module for CE that is mutated in diverse human birth defects.

Introduction

The establishment and maintenance of animal form involves the control of physical forces by molecular systems encoded in the genome, and the elongation of an animal’s head-to-tail body axis is a long-studied paradigm for understanding morphogenesis (Guillot and Lecuit, 2013). This essential step in the construction of a new embryo is driven by an array of morphogenetic engines, including an evolutionarily ancient suite of collective cell behaviors termed convergent extension (Figure 1A; Figure 1—figure supplement 1Huebner and Wallingford, 2018). Critically, failure of axis elongation does not simply result in a shorter embryo, but rather has catastrophic consequences, and defects in convergent extension in mammals, including humans, results in lethal birth defects (Wallingford et al., 2013).

Figure 1 with 3 supplements see all
Vertices bounding shortening v-junctions are physically asymmetric and display heterogeneous fluid and glass-like dynamics.

(A) A four cell T1 transition with mediolaterally (ML)-aligned ‘v-junctions’ (red) and anterior-posterior (A/P) aligned t-junctions (orange) indicated. (B) Frames from time-lapse showing vertex movements of a v-junction; arrows highlight vertices. Frames were acquired at a z-depth of 5 μm above the ECM/coverslip and with a time interval of 2 s. (C) Schematic of asymmetric vertex movements from B; active = red; passive = blue. (D) Vertex motion quantified by the activity parameter, as described in Appendix, Section 1. (N = 42 vertices from 20 embryos; t-test p value is shown). (E) MSD reveals active vertices’ persistent superdiffusive movement (red); passive vertices exhibit intermediate time slowdown (blue). Pink and black display MSD for left and right non-shortening junctions. MSD is described in Appendix, Section 2. (F) MSD from boxed region in E is shown with traces offset for clarity (0.5 for left; 0.65 for right)(N = 20 vertices from 10 embryos).

The biomechanics of convergent extension (CE) and axis elongation more generally have been studied across diverse length scales, providing several key insights (Davidson, 2017; Mongera et al., 2019; Stooke-Vaughan and Campàs, 2018). At the tissue scale, these include quantitative descriptions of patterned macroscopic stiffening (Moore et al., 1995; Zhou et al., 2009), tissue-scale jamming transitions (Mongera et al., 2018; Serwane et al., 2017), and fluid-like multicellular flows (Bénazéraf et al., 2010; Lawton et al., 2013). At smaller length scales, laser ablation studies have provided insights into the patterns of junctional tension within these tissues (Fernandez-Gonzalez et al., 2009; Rauzi et al., 2008; Shindo and Wallingford, 2014). Finally, a more granular examination of the mechanics of CE has been made possible by the use of theoretical modeling (Alt et al., 2017; Fletcher et al., 2017; Merkel and Manning, 2017), with recent innovations continuing to improve these models (e.g. Staddon et al., 2019).

However, our still-emerging understanding of the cell biology of CE continues to present new challenges to understanding its biomechanics. For example, CE is driven by a combination of lamellipodia-based cell crawling by laterally positioned cells and by junction contraction in medially positioned cells (Sun et al., 2017Williams et al., 2014Huebner and Wallingford, 2018). When considering the biomechanics however, very few models consider cell crawling (e.g. Belmonte et al., 2016), with the majority of models addressing only junction contraction. In addition, these junction-contraction models consistently consider individual cell-cell junctions to be mechanically homogenous along their length (Alt et al., 2017; Fletcher et al., 2017; Merkel and Manning, 2017), yet recent work in single cells suggests this approach may be limited. Indeed, there is accumulating evidence that single cells’ membranes can be mechanically heterogeneous (Lieber et al., 2015; Shi et al., 2018; Strale et al., 2015). Thus, the role of mechanical heterogeneity along individual cell-cell junctions during collective cell movement in vivo remains poorly defined.

In addition, we know comparatively little about the interplay of subcellular mechanical properties in vivo and the molecules that govern them. Resolving this disconnect is crucial, because CE in diverse systems is known to require complex spatial and temporal patterns of protein localization and dynamics along individual cell-cell junctions during morphogenesis. For example, the localization and turnover of actomyosin and cadherin adhesion proteins have been extensively quantified during Drosophila CE (Blankenship et al., 2006; Fernandez-Gonzalez et al., 2009; Levayer and Lecuit, 2013; Rauzi et al., 2008), as have similar patterns for the Planar Cell Polarity (PCP) proteins and actomyosin during vertebrate CE (Butler and Wallingford, 2018; Kim and Davidson, 2011; Shindo and Wallingford, 2014). However, the significance of these molecular patterns remains unclear because we lack a similarly granular understanding of subcellular mechanical properties and their dynamics, which ultimately explain the cell behaviors that drive vertebrate CE.

Here, we combine high-speed super-resolution microscopy with concepts rooted in soft matter physics to demonstrate that individual cell-cell junctions in the elongating vertebrate body axis display finely-patterned local mechanical heterogeneity along their length. To explore this unexpected finding, we developed a new theory for junction remodeling in silico and new tools for assessment of very local mechanics in vivo. Combining these, we show that sub-cellular mechanical heterogeneity is essential for CE and is imparted by cadherins via locally patterned intracellular (cis-) interactions. Finally, the local patterns of both cadherin clustering and heterogeneous junction mechanics are controlled by PCP signaling, a key regulatory module for CE that is mutated in diverse human birth defects.

Results

The dynamics of tricellular junction motion during CE suggest an unexpected mechanical heterogeneity at subcellular length scales

The elongating body axis of Xenopus embryos is a long-standing and powerful model system for studying PCP-dependent vertebrate CE (Figure 1—figure supplement 1Huebner and Wallingford, 2018). Xenopus CE can be considered most simply in terms of four-cell neighbor exchanges in which mediolaterally aligned cell-cell junctions (‘v-junctions’) shorten, followed by the elongation of new, perpendicularly aligned junctions (‘t-junctions’)(Figure 1A). To gain deeper insights into this process, we used high-speed super-resolution imaging to establish a quantitative physical description of the motion of tricellular vertices bounding v-junctions (Figure 1B).

First, we found that v-junction shortening was dominated by the movement of a single ‘active’ vertex, while the other ‘passive’ vertex moved comparatively less (Figure 1C,D), similar to the asymmetry observed previously during CE in Drosophila epithelial cells (Vanderleest et al., 2018). To quantify the asymmetric movement of vertices in Xenopus mesenchymal cells, we used a fixed coordinate system and defined an activity parameter, A, as the ratio of the net distance moved by the vertices to the initial junction length, (Figure 1C; Figure 1—figure supplement 2A) (Appendix, Section 1). This analysis demonstrated significant differences in the motion of active and passive vertices (Figure 1D).

We then explored the physical basis of asymmetric motion in active and passive vertices using mean squared displacement (MSD)(SI Section 2). Our analysis revealed that active vertices consistently displayed a highly fluidized movement (i.e. super-diffusive)(Figure 1E,F, red). By contrast, passive vertices displayed the hallmarks of more-constrained, glass-like motion (i.e. defined by sub-diffusive movement with an intermediate time slowdown, as observed in colloidal systems); (Kegel and van Blaaderen, 2000; Weeks et al., 2000Figure 1E,F, blue). The juxtaposition of liquid- and glass-like motion along a single cell-cell junction was interesting, because while fluid-to-glass phase transitions are known features at tissue-level length scales (Angelini et al., 2011; Bi et al., 2015; Malmi-Kakkada et al., 2018; Sinha et al., 2020), such transitions have not been reported at sub-cellular length scales during morphogenesis.

Given these surprising results, we also controlled for the possibility that image drift may interfere with our quantification. To this end, we quantified the motion of active and passive vertices using two relative reference frames with respect to slowly moving landmarks within the tissue (Figure 1—figure supplement 2D–F). All three quantification strategies demonstrate that the asymmetry we observed was not a point-of-reference artifact (Figure 1—figure supplement 2D–G).

Finally, we confirmed the distinct patterns of motion in active and passive vertices using four additional physical metrics, the Van Hove function, the velocity auto-correlation function, the self-overlap parameter, and the fourth order susceptibility, χ4t (SI sections 2-3). All four orthogonal approaches confirmed our finding that the active and passive vertices bounding individual v-junctions exhibit asymmetric dynamic behaviors, with one vertex displaying a fluid-like motion and the other, glass-like (Figure 1—figure supplement 3). Critically, this asymmetric behavior was specific to shortening dynamics of v-junctions, as the two vertices bounding non-shortening junctions in the same tissue were consistently symmetrical, both resembling passive vertices (Figure 1E,F, pink, black; Figure 1—figure supplement 3).

This physical analysis provided three important insights: First, glass-like dynamics previously observed only at tissue-length scales in morphogenesis also exist at the subcellular length scale of individual junctions. Second, the frequently invoked assumption of mechanical homogeneity along single cell-cell junctions, which underlies a wide swath of the biophysical work on morphogenesis, may not be valid. And finally, because only shortening junctions exhibited local mechanical heterogeneities, this phenomenon may be a specific and essential feature of convergent extension.

A new physical model of cell-cell junction remodeling predicts asymmetric, local patterning of junction stiffness as an essential feature of convergent extension

The possibility of mechanical heterogeneity along single cell-cell junctions has important implications, as many biophysical approaches and in silico tools for understanding morphogenesis (e.g. laser cutting, vertex models) assume that junctions are mechanically homogeneous along their length. We therefore developed a new theoretical framework for junction shortening that accommodates the possibility of local mechanical heterogeneity by independently modeling the movement of each vertex (Figure 2A,B; Appendix, Section 4–8).

Figure 2 with 1 supplement see all
A new vertex model incorporating local mechanical heterogeneity recapitulates the fine-scale dynamics of junction shortening observed in vivo.

(A) Sketch of v- junction shortening with elements of the model overlain. Active (red) and passive (blue) vertex movements are affected by a piston modulating the dynamic rest length. The vertices execute elastic motion due to springs of elasticity, kL and kR. L,R indices indicate left and right. The thicker spring indicates a stiffer elasticity constant, kL. (B) Equations of motion for active and passive vertex positions, xL and xR. Displacement of the left (right) vertex due to the piston is determined by the forces FL(FR) whose time dependence is determined by the rest length exponent,ψLψR. The friction experienced by the left (right) vertices are modeled using γLγR. ζL is the colored noise term for the left vertex (Appendix, Section 4-6). (C) Heatmap indicating probability of successful junction shortening (legend at right) in parameter space for the viscoelastic parameter near vertices and the rest length exponent, staying within biologically reasonable values based on data from Drosophila (Solon et al., 2009; Appendix, Section 6). (D) Still image from a time-lapse of Xenopus CE. Insets indicate representative shortening and non-shortening junctions shown in Panels E and F (vertices indicated by arrowheads). (G) Normalized change in length, Ln, for shortening junctions in vivo (black lines) and in simulations using asymmetric viscoelastic parameters (gray lines) resembling the compressed exponential form (red, dashed line) after the time axis is rescaled. (H) Normalized change in length, Ln, for non-shortening junctions in vivo (black lines) and in simulations using symmetrical viscoelastic parameters (gray lines). (I) Quantification of relaxation behavior deviation from the compressed exponential using the residue (Appendix, Section 8-10).

Our model involves (i) a local junction stiffness (or elasticity) modeled using a spring element, which is consistent with the pulsatile relaxation of v-junctions observed in Xenopus CE (Shindo and Wallingford, 2014) (ii) a dynamic rest length, recently shown to be important for modeling CE (Shindo et al., 2019) (iii) a viscoelastic parameter, k/γ, dictated by the spring stiffness, k, and the friction at the vertices,γ; and (iv) a rest length exponent,ψ, which describes the time dependence of plastic displacement of the vertices modeled with a piston (Figure 2A,B; Appendix, Section 4-8).

Using this model, we explored parameter space to find variables in elastic and viscous deformation that can support effective shortening of the junction (Appendix, Sections 7, 8). As shown in the heatmap in Figure 2C, for a given rest length exponent, junctions failed to shorten if the viscoelastic parameter was equal and small for both the vertices (Figure 2C, red box; Appendix, Sections 7, 8). When the viscoelastic parameter was asymmetric, junctions shortened effectively (Figure 2C, gold box). Thus, at the level of binary outcome (i.e. shorten versus fail-to-shorten), our model suggests that CE requires mechanical heterogeneity along single v-junctions.

For a more stringent test, we compared the temporal dynamics of junction shortening in our model to those quantified in vivo from high-speed super-resolution movies (Figure 2D,E). In time-lapse data, the relaxation behavior of v-junctions collapsed into a self-similar pattern when normalized; relaxation became progressively more efficient over time and could be described by a compressed exponential (Figure 2G, black lines; Figure 2—figure supplement 1A,B; Appendix, Sections 9). When the viscoelastic parameters in our model were asymmetric, the shortening dynamics closely recapitulated this compressed exponential relaxation (Figure 2G, gray lines, I; expanded view in Figure 2—figure supplement 1A,B; Appendix, Sections 8–10).

Finally, we also analyzed junction length dynamics in non-shortening junctions in vivo (Figure 2D,F), because unlike shortening junctions, these display symmetrical mechanics along their length (Figure 1E, black, pink). Defining non-shortening junctions as any that displayed no net reduction in length over the observation time scale of ~400 s, we found that the length dynamics of non-shortening junctions in vivo displayed wide fluctuations over time. Moreover, non-shortening junctions did not share a self-similar relaxation pattern and displayed large deviations from the compressed exponential (Figure 2H, black, I; Appendix, Sections 8–10). Likewise, when symmetric viscoelastic parameters (k/γ) were input into the model for both vertices bounding a single junction, the resulting junction length dynamics displayed wide fluctuations in length and deviated substantially from the normal relaxation pattern (Figure 2H, gray; I; Appendix, Sections 8–10).

Thus, by incorporating local mechanical heterogeneity, our new model not only recapitulates overall shortening/non-shortening outcomes, but also quantitatively recapitulates the dynamic patterns of length change observed in both shortening and non-shortening junctions in vivo. Because both modeling and observations suggest a key role for mechanical heterogeneity, we next sought to understand the contribution of such local mechanical regimes to cell movement during CE.

Fluid-like directed motion of active vertices results from restriction of transverse fluctuations in motion

Our theory makes a prediction: that the more fluid-like motion of the active vertex occurs in the context of increased local stiffness (i.e. higher viscoelastic parameter), while the more glass-like motion of the passive vertex occurs in a relatively decreased stiffness regime. Given that vertex movement, while highly directional, is not entirely directed along the line joining two vertices (in-line movement) (Figure 3A), we reasoned that a stiffer mechanical regime might limit the movement of the active vertices perpendicular to the in-line direction; the perpendicular motion is referred to as transverse movement (Figure 3A, green). Transverse movement is indeed limited for active vertices thereby resulting in more smoothly processive, fluid-like motion in the line of shortening as compared to passive vertices (Figure 3A, orange).

Patterns of transverse vertex fluctuations reveal mechanical heterogeneity of active and passive vertices in vivo.

(A) Schematic of transverse fluctuations in the vertex position perpendicular to the direction of junction shortening; traverse movements are extracted using the transverse 'hop' function, which is inversely proportional to the local vertex stiffness (Appendix, Section 12). (B) X/Y coordinates for a representative pair of active and passive vertices color coded for time, with transverse (green) and in-line (orange) motion indicated. (C) Mean transverse fluctuation RT, for active and passive vertices. (N=20 vertices; 10 embryos over 386 seconds; t-test p value shown). (D) Probability distribution of transverse fluctuations, RT, (offset for clarity). (E) Straightness index quantifying the persistence of vertex motion in terms of directionality (Appendix, Section 12); t-test p value is shown. (F) Probability distribution of the straightness index for active (red, offset for clarity) and passive (blue) vertices.

To test our model’s prediction in vivo, we used our time-lapse data to quantify the transverse fluctuations of vertices (Figure 3B, green arrows; Appendix, Section 12). Consistent with our model’s prediction, active vertices displayed significantly less transverse fluctuation than did passive vertices at the same junctions (Figure 3B,C,E), indicating a higher local stiffness at active vertices (Marmottant et al., 2009). Analysis of the straightness index, quantifying how straight vertices move along the in-line direction, independently validated this conclusion (Figure 3E,F; Appendix, Section 12).

This analysis of in vivo imaging data validates our physical model’s prediction of an increased stiffness regime near active junctions and suggests that the lower stiffness regime of passive vertices allows more transverse fluctuation, resulting in less-directed, more glass-like movement. As such, multiple independent lines of observation and theory suggest that local mechanical heterogeneity along cell-cell junctions is a fundamental feature of CE. We next sought to understand the molecular underpinnings of this feature, asking if patterns of protein localization during CE might reflect the local mechanical patterns we identified here.

Patterned cis-clustering of cadherins reflects the heterogeneous mechanics along shortening junctions

We first considered that the observed mechanical asymmetry along shortening v-junctions might result from asymmetric distribution of actomyosin, for example from asymmetric cellular protrusions from neighboring cells or asymmetric junction contraction events along v-junctions. We therefore measured actin intensity in the region abutting active and passive vertices, but we observed no such asymmetry (Figure 4—figure supplement 1A–C).

We next turned our attention to cadherin cell adhesion proteins, which have been shown to tune the very local mechanics of individual cell membranes in culture (Strale et al., 2015). We specifically examined Cdh3, as it is essential for CE in Xenopus (Brieher and Gumbiner, 1994; Fagotto et al., 2013Figure 4—figure supplement 1D) and was recently implicated in CE cell movements in the mouse skin (Cetera et al., 2018). Like all classical cadherins, Cdh3 forms both intercellular trans-dimers and also cis-clusters mediated by intracellular interactions (Figure 4AYap et al., 1997). Such cis-clustering is a key regulatory nexus for cadherin function (Yap et al., 2015), so it is interesting that while the mechanisms governing formation of cadherin cis-clusters during CE has been studied, cis-cluster function during CE remains unknown (e.g. Levayer and Lecuit, 2013; Truong Quang et al., 2013).

Figure 4 with 2 supplements see all
Cadherin cis-clustering correlates with vertex movements and mirrors asymmetric vertex dynamics.

(A) C-cadherin (Cdh3) cis-clustering; trans-dimers form across opposing cell membranes (gray); lateral cis interactions drive clustering. (B) Frames from time-lapse of Cdh3-GFP; white arrows highlight clusters. Dashed lines denote initial vertex positions; yellow arrow indicates junction shortening. (C) Spatial autocorrelation of Cdh3 intensity fluctuations (SI Section 13)(60 image frames, 10 embryos). Autocorrelation decays to zero at ~1 μm. Error bars are standard deviation. (D) Trace from a single v-junction displaying pulsatile shortening highlighted by gray boxes (E) Junction length and Cdh3 cluster size fluctuations for an individual cell-cell junction. Cadherin cluster size fluctuations peak prior to junction shortening events (Appendix, Section 14,15). (F) Heat map showing cross correlation between junction length and Cdh3 cluster size. Color represents the value of the correlation coefficient (legend at right). Dashed black line indicates zero lag time. (Appendix, Section 14,15)(n = 11 junctions and 18 shortening events.) (G) Cadherin cluster size as extracted from spatial correlation curves (Figure 4—figure supplement 2; Appendix, Section 16). Cadherin cluster sizes are significantly larger near active vertices. Clusters near vertices of non-shortening junctions are not significantly different from those near passive vertices.

We used high-speed super-resolution microscopy to image a functional GFP-fusion to Cdh3 and used the spatial autocorrelation function for an unbiased quantification of Cdh3-GFP cluster size (Figure 4B)(Appendix, Section 13). Using this function, an exponential decay in spatial correlation is expected for clusters that are regularly ordered, and this pattern was observed for Cdh3-GFP (Figure 4C). Moreover, this decay reached zero at ~1 μm (Figure 4C), consistent with the size reported for cis-clusters of cadherins in vertebrate cell culture (Yap et al., 2015).

This analysis revealed that together with pulsatile junction shortening (Figure 4DShindo and Wallingford, 2014) Cdh3 clusters undergo dynamic fluctuations in size (Figure 4E). Moreover, fluctuations in mean Cdh3 cluster size significantly cross-correlated with shortening pulses (Figure 4F). Mean cluster size peaked ~20 s prior to the onset of junction shortening pulses (Figure 4E,F)(Appendix, Section 14,15), suggesting a functional relationship between Cdh3 clustering and junction remodeling.

We then reasoned that mechanical heterogeneity observed along cell-cell junctions during CE might be driven by local patterns of Cdh3 clustering, since cadherins can tune the local mechanics of free cell membranes in single cultured cells (Strale et al., 2015). This led us to measure Cdh3 cluster size specifically in the ~3 micron region abutting vertices of shortening v-junctions during shortening pulses. Patterns of Cdh3 clustering were complex and highly heterogeneous, consistent with the mechanical heterogeneities we report here (Figure 4—figure supplement 2). Nonetheless, the mean size of Cdh3 clusters near active junctions was significantly larger than that for clusters near passive vertices (Figure 4G; Appendix, Section 16). We confirmed this important result using an alternative quantification of cluster size involving fits to the exponential decay of the spatial autocorrelation (Figure 4—figure supplement 1E–G; Appendix, Section 16).

Importantly, asymmetric Cdh3 clustering was specific to shortening v-junctions and was not observed along non-shortening junctions in the same tissue. Rather, all vertices bounding non-shortening junctions displayed clustering similar to that near passive vertices in shortening junctions (Figure 4G). Symmetrical clustering in non-shortening reflects the symmetrical dynamics of vertices bounding these junctions, described above (Figure 1E). Accordingly, these results demonstrate that asymmetric cis-clustering of Cdh3 is a specific property of shortening v-junctions during CE and suggests that such clustering may drive the asymmetric mechanics of active and passive vertices that we observed in vivo and predicted in silico.

Cdh3 cis-clustering is required for axis elongation but not homeostatic tissue integrity in vivo

The patterned, asymmetric cis-clustering of Cdh3 during CE is a significant finding, because as mentioned above the function of cis-clustering remains undefined not only for CE, but indeed in any in vivo context. We therefore took advantage of point mutations in Cdh3 that specifically disrupt the hydrophobic pocket that mediates cis clustering, without affecting trans dimerization (cisMut-Cdh3; Figure 5AHarrison et al., 2011; Strale et al., 2015). To test this mutant in vivo, we depleted endogenous Cdh3 as previously described (Figure 5—figure supplement 1Ninomiya et al., 2012), and then re-expressed either wild-type Cdh3-GFP or cisMutant-Cdh3-GFP.

Figure 5 with 1 supplement see all
Cdh3 cis-clustering is required for convergent extension but not homeostatic tissue integrity.

(A) Mutations used to inhibit cadherin cis-clustering. (B) Cdh3-GFP clustering in a control embryo. (C) Cis-clusters absent after re-expression of cisMut-Cdh3-GFP. (D) Mean spatial autocorrelation of Cdh3-GFP intensity fluctuations for wild type (60 image frames, from 10 embryos) and the cis-mutant (56 image frames, five embryos) (Appendix, Section 17). Gradual, non-exponential decay for cisMut-Cdh3-GFP indicates a lack of spatial order (i.e. failure to cluster). (E) Control embryos (~stage 33). (F) Sibling embryos after Cdh3 knockdown. (G) Knockdown embryos re-expressing wild-type Cdh3-GFP. (H) Knockdown embryos re-expressing cisMut-Cdh3-GFP. (I) Axis elongation assessed as the ratio of anteroposterior to dorsoventral length at the widest point. (J) Embryo integrity assessed as percent of embryos alive and intact at stage 23.

We first confirmed the cis mutant’s impact on clustering in vivo. Re-expressed wild-type Cdh3-GFP clustered normally and displayed the expected exponential decay in spatial autocorrelation that indicates regular spatial order and a mean cluster size ~1 μm (Figure 5B,D) (Appendix, Section 13,17). By contrast, when cisMut-Cdh3-GFP was re-expressed, clusters were clearly absent, and the signal was diffuse along cell-cell junctions (Figure 5C). Moreover, the spatial autocorrelation of cisMut-Cdh3-GFP did not decay exponentially (Figure 5D), consistent with a lack of spatial order (Appendix, Section 13,17). We confirmed this result using fits to the exponential decay of the spatial autocorrelation (Figure 7—figure supplement 1) (Appendix, Section 13,17).

We next used the same replacement strategy to directly test the function of cis-clustering in Xenopus CE. At neurulation stages, embryos depleted of Cdh3 display severe defects in axis elongation (Figure 5E,F,I, green) (Brieher and Gumbiner, 1994; Lee and Gumbiner, 1995). At later stages, these embryos disassociate to individual cells due to the widespread requirement for Cdh3 in cell cohesion (Ninomiya et al., 2012Figure 5J, green). We found that re-expression of wild-type Cdh3-GFP rescued both axis elongation and embryo integrity, as expected (Figure 5G,I,J, purple).

Strikingly however, while re-expression of cisMut-Cdh3-GFP significantly rescued overall embryo integrity (Figure 5J, red), it failed to rescue axis elongation (Figure 5H,I, red). These data provide the first experimental test of the role of cadherin cis-clustering in vivo, and moreover, provide an experimental entry point for testing the role of cis-clustering in the generation of local mechanical patterns along cell-cell junctions.

Loss of Cdh3 cis-clustering eliminates mechanical heterogeneity and disrupts shortening dynamics of cell-cell junctions during CE

To understand the relationship between Cdh3 clustering (Figure 4) and the asymmetric mechanics and vertex dynamics of shortening v-junctions (Figures 13), we applied our battery of physical methods to quantify the motion of vertices in cells with disrupted Cdh3 cis-clustering (i.e. Cdh3 knockdown +cisMut-Cdh3 re-expression). We found first that defects in axis elongation in cisMut-Cdh3 expressing cells were accompanied by defects in cell polarization (Figure 6A–C), reflecting the phenotype seen when PCP signaling is disrupted (Wallingford et al., 2000). Second, v-junctions in cells with disrupted Cdh3 clustering displayed large fluctuations in length that deviated significantly from the compressed exponential relaxation pattern observed for normal v-junctions (Figure 6D,E). The aberrant length dynamics of cisMut-Cdh3 expressing junctions resembled those of junctions that lack mechanical heterogeneity (i.e. non-shortening junctions in normal embryos in vivo or those modeled in silico (compare Figure 6D with Figure 2H)).

Cdh3 cis-clustering is required for heterogeneous junction mechanics.

(A) Image of polarized, elongated control Xenopus mesoderm cells. Blue = mediolateral (ML); yellow = anterior-posterior (AP). (B) Stage-matched cells after depletion of endogenous Cdh3 and re-expression of cisMut-Cdh3. (C) Cellular length/width ratio to quantify CE cell behaviors (p value indicates ANOVA result). (D) Normalized junction length dynamics (Ln) for cis-mutant expressing junctions. Large fluctuations here are similar to those seen normally in non-shortening junctions (see Figure 2H). Dashed black line indicates the expected compressed exponential. (E) The residue quantifying significant Ln deviation from the compressed exponential function as compared to control junctions. (F) Plots for transverse fluctuations RT, for control active and passive vertices compared to cis-mutant vertices. (Note: Data for active and passive junctions are re-presented from Figure 3C for comparison.) (G) Schematic illustrating symmetrical vertex behavior after disruption of cdh3 cis-clustering.

We then asked if cisMut-Cdh3 expression also disrupted the normal mechanical heterogeneity of v-junctions by quantifying transverse fluctuations of vertices. We found that all vertices in cells with defective cis-clustering of Cdh3 displayed the elevated transverse fluctuations observed only in passive vertices of normal cells (Figure 6F,G). These results provide direct experimental evidence that Cdh3 cis-clustering restricts transverse movement of vertices, thereby facilitating fluid-like shortening of the junction.

PCP is essential for Cdh3 cis-clustering and mechanical heterogeneity at cell-cell junctions

A key challenge in animal morphogenesis is to understand how ubiquitous cellular machinery such as cadherin adhesion is directed by tissue-specific developmental control mechanisms. PCP signaling is a central regulator of vertebrate CE and PCP proteins localize to shortening v-junctions during Xenopus CE (Figure 7A), where they control actomyosin contractility (Butler and Wallingford, 2018; Shindo et al., 2019), but how these systems interface with cadherin adhesion during CE is poorly defined. Because cells with disrupted Cdh3 cis-clustering superficially resemble those with defective PCP (Figure 6B,C), we asked if Cdh3 clustering may be under the control of PCP signaling.

Figure 7 with 1 supplement see all
PCP is required for cdh3 cis-clustering and heterogeneous junction mechanics.

(A) Cartoon of polarized core PCP protein localization. (B) Still image of Cdh3-GFP after expression of dominant negative Dvl2 (Xdd1). (C) Spatial autocorrelation of Cdh3 intensity fluctuations for Xdd1 (53 image frames, 5 embryos) and control embryos (60 frames, from 10 embryos),± std. dev. The spatial organization of Xdd1 mutant cadherin is similar to cisMut-Cdh3 expressing embryos. (D) Normalized junction length dynamics for Xdd1 embryos. Dashed black line indicates the normal compressed exponential behavior. (E) Residue for the deviation from the universal compressed exponential function for Xdd1 junctions. (F) Plots for transverse fluctuations at active and passive vertices compared to Xdd1-expressing vertices. (Note: Data for active and passive junctions are re-presented from Figure 3C for comparison to Xdd1.) (G) Schematic summarizing the primary conclusions.

We disrupted PCP with the well-characterized dominant-negative version of Dvl2, Xdd1, which severely disrupted cell intercalation behaviors as expected (Wallingford et al., 2000Figure 6C). Strikingly, expression of Xdd1 also elicited a significant disruption of Cdh3 clustering that was apparent in both images and in the lack of exponential decay in spatial autocorrelation data (Figure 7B,C). Finally, Xdd1 expressing junctions also displayed exaggerated length fluctuations, significant deviation from the compressed exponential relaxation behavior, and symmetrical, elevated transverse fluctuations (Figure 7D–F), all features associated only with junctions lacking local mechanical heterogeneity in vivo or in silico.

These data not only provide an independent experimental confirmation of the link between Cdh3 cis-clustering, local mechanical heterogeneity of junctions, and asymmetric vertex dynamics (Figure 7G), but also provide a novel mechanistic link between a conserved and essential developmental regulatory module (PCP), and the ubiquitous machinery of Cadherin adhesion.

Discussion

Here, we combined physical and cell biological approaches to observation, theory, and experiment to identify and link two novel features of vertebrate convergent extension, one physical, the other molecular. First, we show that single cell-cell junctions in vivo display patterned mechanical heterogeneities along their length. Second, we show that locally patterned cis-clustering of a classical cadherin impart these patterns of mechanical heterogeneity under the control of PCP signaling.

These results are fundamentally important, because mechanical homeostasis in tissues is an emergent property of forces interacting across a wide range of length scales, yet we still know little about the subcellular mechanical properties of cells within tissues. Thus, while previous studies describe local heterogeneity in the membranes of single cultured cells (e.g. Lieber et al., 2015; Shi et al., 2018; Strale et al., 2015), our demonstration of local mechanical heterogeneity along single cell-cell junctions in an intact tissue is a substantial advance. Indeed, our data demonstrate that it is not the local heterogeneity per se, but rather its local patterning along individual cell-cell junctions that is a specific and essential feature of the junctional remodeling that drives CE. From a physical standpoint, this insight is important because it implies that the origin of patterned dynamic heterogeneities observed at tissue length scales (e.g. Angelini et al., 2011; Bi et al., 2015; Malmi-Kakkada et al., 2018) may reside in similarly complex patterns at length scales as small as that of individual cadherin clusters.

Our findings are also important for understanding the unifying suite of CE cell behaviors that is deeply conserved across evolution. V-junction shortening is accomplished by a combination of cell crawling via mediolaterally positioned lamellipodia and active contraction of anteroposteriorly positioned cell-cell junctions (Sun et al., 2017; Williams et al., 2014), a pattern that has now been described in animals ranging from nematodes, to insects to vertebrates (Huebner and Wallingford, 2018). Although it remains to be determined whether v-junction shortening in other tissues and animals also displays the heterogeneity we report here, it is nonetheless remarkable that even subtle aspects (e.g. active and passive vertices) are similar in tissues as diverse as Drosophila epithelial cells (Vanderleest et al., 2018) and Xenopus mesenchymal cells (Figure 1). Strikingly, a new preprint reports that asymmetric vertex behaviors are also observed when junction shortening is driven artificially in cultured cells by optogenetic activation of RhoA (Cavanaugh et al., 2021). Moreover, using an entirely independent modeling approach to the one we describe here, that work also suggests that local mechanical heterogeneity in cell-cell junctions is a fundamental feature of cell intercalation (Cavanaugh et al., 2021). Thus, asymmetric junction shortening may have a fundamental physical basis and is clearly ripe for further study.

Perhaps most importantly, our findings also have important implications for cadherin biology. The lateral cis-clustering of cadherins was first described decades ago (Yap et al., 1997) and has been extensively characterized using structural, biochemical, and cell biological approaches (Chen et al., 2015; Fagotto et al., 2013; Hong et al., 2013; Kale et al., 2018; Levayer and Lecuit, 2013; Levayer et al., 2011; Truong Quang et al., 2013; Yap et al., 1998). Because cadherin clustering is thought to be driven by actomyosin contraction (Yap et al., 2015), our finding that PCP signaling is required for normal Cdh3 clustering is important. PCP proteins are enriched at shortening v-junctions, where they control pulsatile actomyosin contractions (Butler and Wallingford, 2018; Shindo et al., 2019; Shindo and Wallingford, 2014). It is reasonable, then, to posit that PCP-dependent actomyosin contraction is the key driver of Cdh3 clustering. However, another PCP protein, Frizzled7, has also been shown to tune cadherin adhesion during Xenopus CE, but bi-fluorescence complementation experiments suggested Frizzled7 inhibits cis-clustering (Kraft et al., 2012). Adding additional complexity is the recent finding that the PCP protein Celsr1, itself an atypical cadherin, not only forms adhesive trans-dimers but also tunes PCP signaling (Stahley et al., 2021). Unraveling the relationship between PCP, cadherins, and cell adhesion is thus an important challenge for future work.

Furthermore, despite the substantial body of work exploring the mechanisms by which cadherin clusters are formed, the functional consequences of defective cis-clustering in morphogenesis, or indeed in any intact tissue, have never been described. Our work therefore fills a critical gap and will be relevant far beyond the context of Xenopus axis elongation; for example Cdh3 (aka p-cadherin) is also implicated in PCP-mediated CE movements in the mouse skin (Cetera et al., 2018).

Our data argue that local asymmetric cis-clustering of Cdh3 is essential for the shortening of cell-cell junctions joining anteroposteriorly neighboring cells. Ultimately, such shortening is the result of the combined action of junction contraction and directed cell crawling (Huebner and Wallingford, 2018). In epithelial cells, contraction occurs apically, while cell crawling acts basolaterally (Sun et al., 2017; Williams et al., 2014). In Xenopus mesenchymal cells, which lack apical-basal polarity, we have found that the two mechanisms are integrated, driving more effective intercalation when both mechanisms act simultaneously (Weng et al., 2021). Another key challenge, therefore, will be to ask how the asymmetry of Cdh3 clustering observed here relates to contraction and/or cell crawling-based intercalation. Our imaging of actin dynamics argues against the simple interpretation that enhanced clustering relates directly to protrusive activity (Figure 4—figure supplement 1). Thus, integrating our findings here with previous work on Cdh3 in lamellipodial protrusions and in tissue boundary formation during Xenopus CE will also be important (see Fagotto et al., 2013; Pfister et al., 2016).

Finally, we note that our work here provides an important complement to the already extensive literature on CE and cadherin function in Drosophila. This is important because unlike all vertebrate animals, PCP proteins are dispensable for CE in Drosophila (Zallen and Wieschaus, 2004). Since PCP-mediated CE is essential for neural tube closure and PCP genes are among the most well-defined genetic risk factors for human neural tube defects (Butler and Wallingford, 2017; Wallingford et al., 2013), our data provide insights that span from the fundamental physics of living cells, to the cell and developmental biology of vertebrate axis elongation, to the etiology of human birth defects.

Materials and methods

Xenopus embryo manipulations

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Ovulation was induced by injection of adult female Xenopus with 600 units of human chorionic gonadotropin and animals were kept at 16°C overnight. Eggs were acquired the following day by squeezing the ovulating females and eggs were fertilized in vitro. Eggs were dejellied in 3% cysteine (pH 8) 1.5 hr after fertilization and embryos were reared in 1/3X Marc’s modified Ringer’s (MMR) solution. For microinjection, embryos were placed in 2% ficoll in 1/3X MMR and then washed in 1/3X MMR after injection. Embryos were injected using a Parker’s Picospritizer III with an MK1 manipulator. Embryos were injected in the dorsal blastomeres at the four cells stage targeting the presumptive dorsal marginal zone. Keller explants were excised at stage 10.25 in Steinberg’s solution using eyelash hair tools.

Morpholino, plasmids, antibody, and cloning

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The Cdh3 morpholino had been previously described (Ninomiya et al., 2012) and was ordered from Gene Tools. Cdh3-GFP, (Pfister et al., 2016) lifeact-RFP, and membrane-BFP were made in pCS105 and Xdd1 was made in CS2myc (Sokol, 1996). Cdh3 antibody was ordered from Developmental Studies Hybridoma Bank (catalog number 6B6). The Cdh3-cis-mutant was generated using the Q5 Site-Directed Mutagenesis Kit (NEB, catalog number A13282) and here we changed valine 259 to aspartic acid and isoleucine 353 to aspartic acid.

Morpholino and mRNA microinjections

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Capped mRNA was generated using the ThermoFisher SP6 mMessage mMachine kit (catalog number AM1340). mRNAs were injected at the following concentrations per blastomere, Membrane-BFP (100 pg), Cdh3-GFP for imaging (50 pg), Cdh3-GFP for rescue (300 pg), Cdh3-cis-mutant (300 pg), lifeact-RFP (100 pg), and Xdd1 (1 ng). Cdh3 morpholino was injected at a concentration of 10 ng per blastomere.

Imaging Xenopus explants

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Explants were mounted on fibronectin coated glass coverslips in either Steinberg’s solution or Danilchik’s for Amy solution. Experiments were repeated in the absence of fibronectin to ensure fibronectin did not confound results. Explants were incubated at room temperature for 4 hr or at 16°C overnight before imaging. Standard confocal images were acquired with either a Nikon A1R or a Zeiss LSM 700. Super-resolution images were acquired with a commercially available instantaneous structured illumination microscope (BioVision Technologies). Standard confocal time-lapse movies were acquired with a 20 s time interval and super resolution images were acquired with a 2 s time interval. All images were acquired at a z-depth of 5 μm above the coverslip to insure similar z-depth sampling between images.

Measurement of Cdh3 intensity at cell junctions

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All image analyses were performed using the open-source image analysis software Fiji (Schindelin et al., 2012). Images were first processed with 50-pixel rolling ball radius background subtraction and smoothed with a 3 × 3 averaging filter, which allowed better distinction of individual cadherin clusters. The segmented line tool, with width set to the thickness of the junction (~16 pixels), was used to set a line of interest (LOI) across the length of the cell junction. Next the multi-plot tool was used to extract cdh3 intensity values across the length of the cell junction and the measure tool was used to collect data such as junction length and mean intensity values. The Fiji Time Lapse plugin Line Interpolator Tool was used to make successive measurements for movies. Here a segmented line LOI was drawn every 10–30 frames, the line interpolator tool was then used to fill in the LOIs between the manually drawn LOIs allowing rapid semi-manual segmentation. The multi-plot tool and measure tool were then used to extract data for each time-point of the movie. Source data for all imaging experiments can be found in the Dryad Server (doi: 10.5061/dryad.pg4f4qrph).

Cdh3 immunostaining

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Samples were prepared by micro-dissection as described above and incubated at room temperature for 4 hr or overnight at 16°C. Samples were then fixed in 1x MEMFA for 1 hr at room temperature and washed three times with PBS to remove fixative. Next samples were permeabilized with 0.05% Triton X-100 in PBS for 30 min and then blocked in 1% normal goat serum (NGS) in PBS for 2 hr at room temperature. The primary antibody was then diluted 1:100 in fresh 0.1% NGS/PBS and samples were incubated with primary antibody at 4°C overnight. Samples were then blocked a second time at room temperature for 1 hr and then washed twice with fresh blocking solution. Secondary antibody (goat anti-Mouse 488, #A32723) was diluted 1:500 and samples were incubated at 4°C overnight. Finally, samples were washed three times in 1X PBS and imaged.

Embryo length to width measurement

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Embryos were injected in the dorsal blastomeres with Cdh3-MO, Cdh3-MO + Cdh3 GFP (rescue), Cdh3-MO + Cdh3 cis-mutant (mutant),or left as un-injected controls. Live embryos were kept at room temperature for 26 hr post fertilization (~stage 33). Embryos were then fixed with MEMFA in glass vials on and rotated for 1 hr at room temperature. Post fixation samples were washed three times in 0.1% Tween-20 in 1X PBS and then images of embryos were acquired using a Zeiss AXIO Zoom stereoscope. The embryos anterior-posterior length and dorsal-ventral width were then measured using Fiji.

Embryo survivability assay

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Embryos were injected in the same manner as done for the length to width measurement and the number of embryos injected for each condition was recorded. Embryos were then kept at room temperature for 20 hr (~stage 20) and the number of surviving embryos was recorded. The percentage of embryos surviving (embryo integrity) was reported.

Measurement of Cdh3 knockdown efficiency

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Embryos were injected at the four-cell stage in a single dorsal blastomere with Cdh3-MO + membrane BFP generating embryos with mosaic knockdown of Cdh3 on the dorsal side of the embryo. Explants were next dissected from embryos, immuno-stained for Cdh3, and images were acquired as described above. The mosaic labeling allowed us to compare wild type and Cdh3-KD cells (marked by membrane-BFP) within a single explant. First, we used Fiji to measure endogenous Cdh3 intensity at cell junctions in wild type and Cdh3-KD cells and used a t-test to statistically compare these conditions. Next cellular polarity was assessed for each condition by measuring the ratio of the mediolateral length to the anterior-posterior width of individual cells.

Appendix 1

Section 1. Active versus passive vertex dynamics

We used the Manual Tracking plugin in FIJI to obtain the trajectories of vertex pairs. Individual vertex positions were tracked for a time interval of 400 s every 2 s. By obtaining the time-dependent two-dimensional (2D) vertex co-ordinates (xL,yL) and (xR,yR) for the left (L) and right (R) vertices respectively, the net distance travelled by the left(L) vertex is,

(1) ΔrL=(xL(tf)xL(t0))2+(yL(tf)yL(t0))2,

where xL(tf), xL(t0) are the vertex positions at the final (tf) and initial time (to) of measurement respectively. A similar equation with xR,yR applies for the right vertex. The length of the junction is,

(2) L(t)=(xR(t)xL(t))2+(yR(t)yL(t))2

To determine the weight of the contribution of each vertex to junction shortening, we define an activity parameter, A, as the ratio of net vertex distance moved to the initial junction length that is AL=ΔrLL(t0). Similarly, AR=ΔrRL(t0), for the right vertex. If AL>AR, the left vertex is labelled as the ‘active’ vertex while the right vertex is the ‘passive’ one, and vice versa if AR>AL. Over the time frames that we have analyzed the vertex movement, the median value of L(tf)/L(t0)~ 0.30, implying that the junctions have shortened by 70% as compared to the initial junction length. Both high time resolution (2s per frame) and low time resolution (20s per frame) imaging data show the same trend that one of the vertices tend to be active, contributing more to junction shortening (Figure 1B–C, Main Text). We confirm that this observation is not due to the overall motion of the cells as detailed below (Figure 2—figure supplement 2).

Section 2. Quantifying the heterogenous dynamics of vertices: Mean Square Displacement (MSD), van Hove function, and the velocity autocorrelation

The characteristics of vertex dynamics could provide clues as to the active mechanisms that promote or impede vertex movement. An important parameter to quantify vertex dynamics is the Mean Square Displacement (MSD), as a function of the lag time t. Time averaged MSD, Δ-ti, is calculated using the vertex positions rit',

(3) Δ(t)L,i=1Tt0Tt|rL,i(t+t)rL,i(t)|2dt

where T=400s and subscript L stands for the left vertex. Taking the average over N independent vertex trajectories, labelled by the index i, we obtain the ensemble averaged MSD,ΔtL=1Ni=1NΔ-(t)L,i. The same procedure is used to calculate the MSD for the right vertex (see Figure 1E, Main Text). In many physical systems, the MSD increases with a power law, that is. Δt~tα. When the vertex motion is uncorrelated in time and along random directions, the dynamics is described as Brownian, and the MSD exponent is unity, α=1. Sub-diffusive, α<1, movement occurs when there is a hindrance to motion or the dynamics is highly correlated. For example, when a particle in caged by its immediate neighbors, sub-diffusive motion results. Super-diffusive MSD, α>1, is seen when the motion is highly directed.

We found substantial heterogeneity in the individual vertex MSD as seen from the plot of Δ-ti (Figure 14—figure supplement 2C). Active and passive vertex MSDs span 3 orders of magnitude of time lag. Two distinct time regimes are observed for both active and passive vertex movements: (i) at short time lags, t<30s, active and passive vertex movements are random, characterized by MSD exponent α~1. (ii) For t>40s, active vertices show strong superdiffusive movement while passive vertices undergo a slowdown followed by a recovery toward superdiffusive motion (see Figure 1E,F Main Text). These distinct differences between active versus passive vertices are observed in the ensemble averaged MSD, Δ(t) for 20 vertices from 10 different embryos.

To eliminate the effect of motion of the entire tissue, we tracked vertex positions with respect to the center of an egg yolk particle (Figure 1—figure supplement 2D, E) typically present within cells as well as nearby stationary vertices (Figure 1—figure supplement 2F, G). In this manner, we analyzed the relative vertex positions, rrel, with respect to a frame of reference within the tissue being imaged. By extracting the co-ordinates of the center of an egg yolk within a cell or nearby vertices, rc, we obtain the relative vertex positions, rrel,L=rL-rc. We then evaluated the mean square relative displacements (MSRD) for the left and right vertex pairs using Equation (3) above (Figure 1—figure supplement 2E, G). The distinct differences between active versus passive vertex dynamics is conserved in this relative co-ordinate system, indicating that the asymmetry in active versus passive vertex movement is not due to motion of the whole tissue (see Figure 1—figure supplement 2D, G).

Van Hove function

Insights into vertex motion may be obtained by analogy to spatially heterogenous dynamics in supercooled liquids (Barrat et al., 1990; Thirumalai and Mountain, 1993). The distribution of particle displacements is expected to be a Gaussian in simple fluids. In supercooled liquids, however, the displacements of a subset of particles deviate from the Gaussian distribution (Thirumalai and Mountain, 1993). From the distance moved by a vertex during the time interval δt, defined as δriδt=|rit+δt-rit|, the van Hove function for vertex displacement (or the probability distribution of vertex step size) is,

(4) Pδrδt=1Ni=1Nθ(δri-rit+δt-rit)

where the average is over N independent vertex trajectories. The van Hove distribution at δt=40s, for active (red) and passive vertices (blue) is shown in (Figure 1—figure supplement 3A). The 40s time interval is long enough to clearly observe the differences in the distances moved by active and passive vertices. The van Hove distribution at δt=4s is shown in (Figure 1—figure supplement 3B). At this short time interval, distances moved by active and passive vertices are similar and is well fit by a Gaussian (see inset Figure 1—figure supplement 3B). However, the van Hove distribution deviates significantly from the Gaussian distribution at δt=40s (see inset Figure 1—figure supplement 3A), indicating the growing heterogeneity in the vertex displacements.

Average velocity distribution and velocity autocorrelation function (VACF)

To further quantify the striking differences in the movement of active and passive vertices, we calculate the average velocity of the vertices. The average velocity over a time interval τ is defined as,

(5) vL(τ)=rL(t)rL(t+τ)τ

Replacing rL by rR gives the average velocity of the right vertex. We analyze the average velocity over a time interval τ because experimental data is also an average over the time resolution of the iSIM microscope. We then compare the speed distribution (|vL(τ)|) of active and passive vertices over both short, τ=4s (Figure 1—figure supplement 3C, blue for passive and red for active vertices) and longer time intervals, τ=60s (Figure 1—figure supplement 3D). At the smaller time interval, τ=4s, the speed distribution of active and passive vertices are similar. This indicates minimal differences between active and passive vertex dynamics at short time scales. The difference in active and passive speed distribution is, however, pronounced at τ=60s. The passive vertex speed distribution peaks at a smaller value and decays rapidly for larger speed values, compared to active vertices. This illustrates the fluidization in the movement of active vertices that develops over a time scale of order 50s in agreement with other measures such as the MSD and the van Hove distribution as reported above.

To probe the time interval over which the average velocity (at fixed τ) is correlated with average velocity at a time point separated by δt, we calculate the velocity autocorrelation function (VACF),

(6) Cvτ(δt)=v(t+δt).v(t)

where the average is defined as =1T-δt0T-δtdt. The VACF is normalized such that Cvτδt=0=1. At the shorter time interval of τ=4s, VACF for active and passive vertices exhibit a rapid decay to zero (Figure 1—figure supplement 3E), blue for passive and red for active vertices. Individual vertex VACF are plotted in transparent colors and the mean as dashed lines (blue-black dashed line for passive vertices and red-black dashed line for active vertices).

Analyzing vertex velocities at τ=60s clearly brings out the different dynamics that characterize active versus passive vertices (Figure 1—figure supplement 3F, blue for passive and red for active vertices). Velocity correlations decay quicker for passive vertices, becoming negative and then rebounds. However, active vertex velocity correlations are more persistent with time as evident from the longer time to decay.

Section 3. Self-overlap parameter and dynamic heterogeneity

To quantify the highly asymmetric vertex movement that underlies CE, we measured the fractional change in vertex positions over a time interval t using the self-overlap order parameter, defined as:

(7) Q(t)=1NiNwi

where wi=1 if |ri(t+t)ri(t)|<Lc and wi=0 otherwise. The self-overlap parameter is dependent on the length scale that is probed by Lc and represents the probability that vertices have moved by a specified length scale over a time interval, t. We chose Lc=1.3μm, as this is the distance scale over which movement of active and passive vertex become distinct. This is evident from the plot of MSD (Figure 1E,F, Main Text) for active and passive vertices where the dynamics begins to differ at a length scale of >1μm. If a vertex moves less than Lc=1.3μm over the time interval t, the vertex is considered to have 100% overlap with its previous position, and hence assigned a value 1. However, if the vertex has moved more than 1.3μm within the time interval t, we consider this as 0% overlap. The self-overlap function, Qt, is calculated by averaging over a range of initial times, t', followed by ensemble averaging over individual vertices (Figure 1—figure supplement 3G-H). The active vertex self-overlap function decays rapidly and can be fit to a single exponential decay function, indicating liquid like dynamics. However, passive vertex overlap function shows a two-step decay, a signature of glass-like dynamics (Figure 1—figure supplement 3G).

Although the MSD and the self-overlap function Qt are useful to quantitatively characterize vertex movement, other metrics are needed to gather further insights into the dynamic heterogeneity and correlations in vertex movement that emerge temporally during CE. In systems approaching the glass transition, the cooperativity of motion increases such that the length and time scales characterizing the dynamic heterogeneity are expected to grow sharply. In supercooled liquids, the fourth order susceptibility, χ4t, provides a unique way to distinguish the dynamic fluctuations between liquid and frozen states (Kirkpatrick and Thirumalai, 1988). Therefore, we compute the fourth order susceptibility from the variance of the self-overlap parameter,

(8) χ4(t)=Q(t)2Q(t)2

Similar to structural glasses, the dynamic heterogeneity, quantified by χ4t increases with time, peaks at a maximum time interval, tM and then decays (Figure 1—figure supplement 3I). The dynamic heterogeneity is manifested as dramatic variations between individual vertex trajectories in both active and passive vertex movements. For active vertices, χ4t peaks at tM~120s while for passive vertices heterogeneity peaks at a longer time interval tM~170s (Figure 1—figure supplement 3l). The time scale associated with the peak in dynamic heterogeneity is consistent with the viscoelastic relaxation time (further discussed below), known to be the characteristic relaxation time for vertices connected by the cell cortex under tension (Solon et al., 2009). For non-shortening junctions, χ4t, does not show a peak (Figure 1—figure supplement 3J). We anticipate the peak to be at a much longer time scale for vertices of non-shortening junctions.

Section 4. Theoretical model

Vertex based models are important for studying the dynamics of confluent cell layers (Fletcher et al., 2014). The junction between three or more cells (vertices) are represented as point particles. The connecting edge between vertices represent cell-cell interfaces. We developed a theoretical model for junction shortening to understand the asymmetric dynamics of vertices. Our model, shown in (Figure 2A,B Main Text), is a coarse-grained representation of a collection of cells intercalating mediolaterally. Each vertex, bounding the v-junction, are connected to Maxwell-like components with viscous and elastic elements. Elastic properties are modeled by springs with stiffness, k, and actuators characterize the viscous motion of cell vertices (see Figure 2A Main Text; γ is the viscosity). For the purposes of visualization, we depict the spring-actuator element as being in the direction away from the cell-cell interface, exerting a compressive force on the vertices. This need not be the case as the forces and mechanical factors contributing to junction shortening can also be localized within the cell-cell junction. For the purposes of simplicity in visualization, we picked a direction for the spring-actuation element.

We assume that the position of the left vertex, rL(xL,yL), evolves according to the equation of motion:

(9) drLdt=kL.rLγL+FLγL+ζL

where kL is the elasticity of the left (L) vertex, FL is the contractile force responsible for viscous deformation of the vertex and γL is viscosity coefficient of the vertex. Replacing the subscript L with R above gives the equation of motion for the right vertex. The local elasticity near the vertices are accounted for by a connected harmonic spring with strength kL. The spring is connected in series with an actuator that supplies the contractile force, FL. It is likely that the noise in a physical or biological system is correlated in time. Consistent with our observation that fluctuations in junction length are correlated in time, we model ζL as the colored noise experienced by the vertices. The noise, ζL, represents the coupling of the vertices to their immediate local environment, satisfying ζLtζLs=Ae-|t-s|/τn with the mean ζLt=0. The coefficient, A, is the noise strength. For large noise strength, vertex positions show large amplitude deviations from the position dictated by the minimum of the elastic force, as constrained by the spring. For small persistence time of the correlated noise, τn, the vertex dynamics is highly uncorrelated in time. At large persistence times, however, the noise induced fluctuations in the vertex positions are correlated over the timescale τn. We set the noise correlation time to be the persistence time of junction length fluctuations. The colored noise satisfies, dζLdt=-ζLτn+1τnη(t), where η(t) is the Gaussian white noise source characterized by delta correlation ηtηs=δ(t-s) and mean η=0.

Since the movement of vertices along the medio-lateral direction is much more persistent as opposed to the perpendicular direction, as evident from the closure of junctions, we simplify the model to consider only one-dimensional (1D) motion. Henceforth, we drop the vector notation and focus on the vertex dynamics along the x-axis.

By considering the basic vertex equations in the Langevin picture,

(10) dxLdt=kLγL×(xLaLtψL)+ζL
(11) dxRdt=kRγR×(xR(L0aRtψR))+ζR

we model the vertex equations of motion in analogy to particles moving in a translating optical trap. The minimum of the left elastic ‘trap’ changes dynamically due to the term aLtψL in Equation 10 (modeled by the left actuator). Similarly, the right elastic ‘trap’ is translated from its initial position L0 by aRtψR in Equation 11 (modeled by the right actuator). These terms serve as a proxy for active contractile forces which viscously deform the cell edges. Hence, we refer to the exponents, ψL and ψR, as the rest length exponents. The physical implication of the rest length exponent is that the rest length of the junction varies dynamically. The contractile force is, FL,total=V(xL) in Equation 9, where V(xL) is the time-dependent ‘trap’ potential of the form VL=0.5kLxL-aLtψL2 and VR=0.5kRxR-L0-aRtψR2. The stochastic movement of the vertices in a translating potential leads to a ratchet-like effect where the vertex dynamics has a specified direction. This directionality in the motion of the vertices does not arise, however, from the asymmetry in the potential but rather from the asymmetric translation of the potential well minimum or the dynamic rest length.

Hence, the active time-dependent forces contributing to junction shortening were modeled in silico as,

(12) FL(t)=kLaLtψL
(13) FR(t)=kR(L0aRtψR)

where aL and aR are the ‘acceleration’ of the left and right vertices respectively, and the exponents ψL and ψR determine the temporal dynamics of the contractile force. We include the acceleration term to account for the experimentally observed increase in the persistence of junction shortening as a function of time (see Figure 2G Main Text; See also Sec. 9 below). The initial condition is set as xLt=0=0, and xRt=0=L0, with L0 being the initial cell-cell junction length. We arbitrarily assign the left side to be active, with the time dependent active force rising in proportion to tψL(ψL>ψR). The right side is assigned to be passive, with force increasing with time as tψR. The difference in the rest length exponents, ψL versus ψR, determines which vertex is active.

The equations of motion then become:

(14) dxLdt=kLγLxL+kLaLtψLγL+ζL
(15) dxRdt=kRγRxR+kR(L0aRtψR)γR+ζR

Defining x-L=xLx0, t-=tτ and a-L=aLaL0, where x0=10μm, τ=102sec and aL0τψL=x0, we recast the equations of motions into dimensionless forms. Similar normalization with L replaced by R applies for the right vertex. The system of equations is scaled with the characteristic length and time, x0 and τ, physiologically relevant for cells undergoing convergent extension. In terms of the normalized quantities, the equation of motion is,

(16) dxLdt=1τL×(xLaLtψL)+ζL
(17) dxRdt=1τR×(xR(L0aRtψR))+ζR

where the parameter kLγL=1τL has the dimension of inverse time 1s. When normalized by the characteristic timescale τ, ττL=τ×kLγL=1τ-L, we obtain a dimensionless parameter which we refer to as the viscoelastic ratio.

Section 5. Dynamic rest length and colored noise

In vertex-based models for plant cells, the cell-cell interface length is modeled with a spring having a characteristic rest length (Merks et al., 2011). Any deviation in the length of the cell-cell interface from the rest length is energetically unfavorable. In vertex models for animal cells, such a rest length is typically not included (Fletcher et al., 2014). In our coarse-grained vertex model, we include a spring term with dynamic rest lengths. We show that this model accounts for the asymmetric vertex dynamics and quantitative experimental features of the junction shortening behavior. By studying actomyosin contractility in combination with theoretical modeling, it has recently been shown that epithelial junctions exhibit both elastic and viscous remodeling behavior (Staddon et al., 2019).

The existence of memory effects in junction shortening necessitates the addition of the colored noise term. Previous vertex-based models have considered random white noise indicating no memory effect. However, by experimentally quantifying the junction length fluctuations, we would like to point out that colored noise may be important to consider in modeling biological systems.

Section 6. Parameter values for elasticity and viscosity:

The viscoelastic ratios, 1/τ-L and 1/τ-R, were varied from 0.05 to 5 equivalent to 5×10-4s-1-0.05s-1 in dimensional units. Therefore, the viscoelastic relaxation time is in the range of 20s-2000s. Spring stiffness, k, in the range between 100pN/μm and 1nN/μm (Bittig et al., 2008; Girard et al., 2007) and the viscosity, γ~100nN.s/μm (Forgacs et al., 1998), accounts for the elastic and viscous properties of tissues previously reported in the literature. For these values, one obtains the viscoelastic relaxation time in the range of 1s-100s. Therefore, the viscoelastic ratio used in our model is within an order of magnitude of the physiological values for both tissue stiffness and viscosity.

Section 7. Simulation details

We consider a wide range of values for both the viscoelastic ratio and the rest length exponent for the active vertex, ψL. The time step in the simulation is Δt=0.0022=0.22s, chosen to be smaller than the characteristic viscoelastic relaxation time (of order 10s). We evolve the simulation for a total of n=20, 000 steps (4, 400s in real units). The equations of motion are solved using the Euler method for each vertex. If at any point during the simulation, the left and right vertex positions approach one another to a distance less than 0.5μm, we label the junction as having successfully completed the shortening. The initial junction length was set to be L0=2, equal to 20μm in real units. The range of rest length exponents we consider is limited by the need to ensure that the minima of the potentials do not overlap during a given simulation run. To generate the phase diagram for the probability of junction shortening as a function of the rest length exponent and the viscoelastic ratio, we consider for the left active vertex 0.051τ-L5 at intervals of 0.5. Rest length exponents in the range, 1.7 <ψL<2, were simulated at intervals of 0.25 for the active vertex. ψR=1.3 is fixed for the passive right vertex. The acceleration of the potential minima, is set to be a-L=a-R=0.001. The viscoelastic ratio for the right passive vertex is fixed at 1τ-R=0.1. We simulated 100 junction shortening events at each value of the parameters kLγL and ψL. By monitoring the percent of successful junction shortening events, we generate the phase diagram (Figure 2C, Main Text).

Section 8. Effect of viscoelasticity on the shortening of junctions

We observe in the phase diagram (Figure 2C, Main Text) that at a fixed value of the rest length exponent, modulating the asymmetry of the viscoelastic parameter ((kLγL)/(kRγR)) leads to a transition from non-shortening (failure to shorten) to junction shortening (successful shortening) regime. At constant ψL=1.95, for low values of the active vertex viscoelastic parameter (τ¯R/τ¯L)<6.9, less than 40% of the junctions shorten. However, at higher values of the viscoelastic parameter, τR/τL>15, more than 80% of the junctions successfully execute shortening. Therefore, the theory predicts that the asymmetry in local viscoelasticity is critical for cells to intercalate medially and effect convergent extension. We calculate the normalized length for non-shortening junctions and found that the self-similarity in junction length dynamics is broken, in agreement with experimental results Figure (2H,Main Text). Ln for non-shortening junctions is characterized by large fluctuations away from the expected compressed exponential behavior, as quantified by the residue (see details below). Simulated junction length dynamics for the non-shortening case(gray curves in Figure 2H Main Text) is obtained for parameter values 1/τ-L=0.05, 1/τ-R=0.05 and ψL=2,ψR=1.3. Meanwhile, for the shortening phase (gray curves in Figure 2G Main Text), 1/τ-L=5, 1/τ-R=0.05 and ψL=2,ψR=1.3. Therefore, asymmetry in viscoelasticity is critical for junctions to execute shortening. Our model points out that the persistent dynamics of active vertices, enabling the efficient shortening of the cell-cell interfaces, is a direct consequence of the faster viscoelastic relaxation time.

Section 9. Normalized junction length dynamics

We calculated the normalized cell-cell junction contact lengths to characterize the self-similarity in the length change underlying cell neighbor exchanges during convergent extension. We selected all cell-cell contacts that shorten over time intervals > 100 s, and normalized the change in length as,

(18) Ln(t)=Lt-LtfLt0-Ltf

where L(tf), L(t0) are the junction lengths at the final and initial time points respectively. The normalized junction length dynamics, Lnt, provides insight into the active processes that underlie vertex movement driving CE. Since junction lengths are highly heterogeneous (Figure 2—figure supplement 1A) relative to, L(t0), and the time to closure, tf-t0, the normalization in Equation 18 allows us to rescale all the length changes to values between 1 and 0. The normalized length curve was smoothed (over 10-time frame windows = 20s) to remove higher frequency noise. To determine if junction shortening exhibits a self-similar behavior across multiple embryos, we rescaled the time axis in Ln(t) by the relaxation time τf, defined as the time at which Ln(t=τf)= 0.3. This corresponds to a 70% reduction in the junction length. Rescaling the time axis by t/τf collapses the normalized lengths onto the functional form,

(19) Ln[t/τf]=e1.5(tτf)3.8

which is a single compressed exponential (Figure 2—figure supplement 1B). The extent of the self-similarity is striking in comparison to both non-shortening (Figure 2H, Main Text) and cis-mutant normalized junction lengths (Figure 6D, Main Text). Notice that for t<τf, change in normalized junction length is slower than exponential decay. However, for t>τf, normalized junction length shortens significantly faster than would be predicted based on exponential decay. Therefore, the compressed exponential behavior for Ln provides evidence that the persistence of junction shortening increases with time.

Section 10. Residue

We quantify the deviation of the normalized junction shortening from the expected compressed exponential behavior by calculating the rescaled time, tr=tτf, and ω=|e1.5(tr)3.8Ln|, where ω is the residue. τf, is defined as the time at which Ln(t=τf)= 0.3. In (Figure 2I, Main Text), non-shortening junctions show strong deviations from the expected compressed exponential behavior while shortening junctions closely follow the compressed exponential form.

Section 11. Alternative form of the contractile force

To test the robustness of the conclusions obtained using our model, we consider an alternative form of the contractile force experienced by the vertices. We model the actuators contributing to viscous junction shortening as moving with constant velocities - v-L and v-R- for the left and right vertices respectively:

(20) dxLdt=1τL×(xLvLt)+ζL
(21) dxRdt=1τR×(xR(L0vRt))+ζR

The ‘trap’ potential in this scenario is of the form, VL=kLxL-vLt2 and VR=kRxR-L0-vRt2, moving with constant velocities. Left vertex is defined to be active with vL> v-R. The velocity is normalized as v-L=vL/(x0τ). The passive vertex velocity is fixed at v-R=0.011, which in dimensional units correspond to 0.0011μm/s. The active vertex velocity is varied in the range of 0.03v-L0.034, which in dimensional units is between 0.003μm/s - 0.0034μm/s. Experimental vertex shortening velocities in the range of 0.001μm/s to 0.021μm/s was reported by some of us in a previous work (Shindo and Wallingford, 2014). Fixing the passive viscoelastic ratio at, 1/τ-R=0.1, we varied 0.051/τ-L5 for the active vertex. Keeping all the other parameters the same, we arrive at the same conclusion that local junction viscoelastic response is critical to effect junction shortening (Figure 2—figure supplement 1D). Therefore, our conclusions are not affected by the specific form of the vertex dynamics. A crucial aspect is that the two potential well minima should move asymmetrically in time.

Section 12. Transverse fluctuations of the vertices and Straightness Index

We quantify the intermittent movement (See Figure 3A, Main Text) of the vertices perpendicular to the motion that contributes to the junction shortening by calculating the transverse fluctuations, RT. The transverse step size is given by, δrTt=δrL(t)sinθ, where δrLt=rLt-rLt-δt and the angle θ is the obtained from the dot product, δrT.ΔrL=|δrT||ΔrL|cos(θ). Here, the net displacement of the Left(L) vertex is given by, ΔrL=(xL(tf)xL(t0))x^+(yL(tf)yL(t0))y^. Similar equation applies for the right vertex with xL,yL replaced by xR,yR. To better quantify the intermittent dynamics, we compute the transverse 'hop' function,

(22) RT(t)=(δrT(t)δrTB)2

The angular bracket above ..B denote the average over the time window Bt-δt,t+δt. We chose for the hop duration parameter, δt=4s, to probe short time transverse fluctuations. The probability distribution of all RTt values are shown in (Figure 3D, Main Text). By averaging the transverse fluctuations over all vertices, RTt=1Ni=1NRTti, we obtain the mean transverse fluctuation for active and passive vertices (Figure 3C, Main Text). RTt for Cis-mutant and Xdd1 vertices are shown in Figure 6F and Figure 7F of the Main Text, respectively.

Straightness index

The directionality of the vertex trajectories were assessed using the straightness index. This is defined as the ratio of the net distance moved by a vertex between initial and final time points to the total distance moved by a vertex:

(23) StraightnessIndex=|r(tf)r(to)|Σt|r(t+δt)r(t)|

Higher the value of the straightness index, the more directed the movement is with the value of straightness index = 1 indicating perfectly straight line motion (see Figure 3E, Main Text).

Section 13. Cadherin clustering from the spatial autocorrelation function

To determine the characteristic spatial correlation of cadherin intensity fluctuations, we analyze the pixel-by-pixel Cadherin3 (Cdh3) intensity data, I(ri), along the medio-lateral cell-cell interface (v-junction). Here, ri is the position of the i-th pixel in the iSIM image. The spatial autocorrelation function of the cadherin intensity fluctuations as a function of distance, r, along the cell-cell interface is,

(24) C(r)=i,jθ(r|rirj|)[(I(ri)I)(I(rj)I)I2I2],

where θz=1 if z=0, θz=0 for any other value of z. I is the mean cadherin intensity over all the pixels along the cell-cell junction. C(r) is normalized such that Cr=0=1. The cadherin correlation length is defined as the distance, ξ, at which Cr=ξ=0. This provides a measure of the distance scale at which the correlation in cadherin intensity fluctuations is lost. Equivalently, ξ, sets the spatial persistence of cadherin fluctuations along the cell-cell junction, providing a quantitative measure of lateral cadherin clustering. We analyzed cadherin clustering patterns along individual cell-cell junctions separately at time intervals of 2s and obtained the spatial correlation behavior for individual junctions from 10 embryos. The mean of the cadherin spatial correlation (over 100s of time points) for wild type embryos is reported in Figure 4C, Main Text with the error bar denoting the standard deviation. To analyze the dynamic variation in cadherin cluster size as a function of time, Cr, was calculated over a time interval of 320s at 2s resolution. The fluctuation in cluster size is given by, δξ(t)=ξ(t)-ξt, where ξt is the mean cluster size over the analyzed time interval (, 4E Main Text). The cluster size fluctuation, δξ(t), was smoothed (over 10-time frame windows = 20s) in order to remove high frequency noise.

Section 14. Junction length fluctuations

To analyze the instantaneous change in the junction length, we calculated, δLt=(Lt-Lt+δt), where δt=2s and t is the time. The unit of the length fluctuations is μm. When the junction shortens, δL(t)>0, while extension implies δL(t)<0 (Figure 4E, Main Text).

Section 15. Cross-correlation between cadherin cluster size and the junction length fluctuations

The normalized cross-correlation between junction length fluctuations, δLt, and cadherin cluster size fluctuations, δξt, was calculated in MATLAB using,

(25) CδL,δξ(τ)=0Tδξ(t)×δL(t+τ)dt,

where T is the total time of analysis and τ is the lagtime. We analyzed the cross-correlation for 18 junction shortening events and show the correlation coefficient as a heatmap in Figure 4F, Main Text

Section 16. Asymmetry in cadherin clustering:

To quantify the asymmetry in Cdh3 clustering in the spatial region near the left and right vertices, we calculated the spatial correlation in cadherin intensity fluctuations, Cr (see Equation 24), in a region spanning 3.25μm adjacent to left and right vertices. The spatial region is chosen such that on average it is 3X larger than typical cadherin cluster size of order 1μm. The localized cadherin clustering behavior adjacent to active and passive vertices, quantified by the spatial correlation in cadherin intensity fluctuations, is shown in Figure 4G Main Text. Main Text also compares the local cadherin clustering behavior in non-shortening junctions to shortening junctions.

We then wondered if spatial correlation in cadherin expression is stable in time across a single cell-cell junction. We computed the spatial cadherin correlation at 2 second time intervals along single cell-cell junctions from multiple embryos. Our results indicate that the spatial correlation length of cadherin expression is highly heterogeneous in time, with the correlation length varying from 0.2 μm to 1.6 μm, as shown in Figure 4—figure supplement 2. To decipher how the spatial correlation in cadherin expression along the cell-cell junction varies with time near active and passive vertices, we present the data for spatial autocorrelation of cadherin fluctuations in Figure 4—figure supplement 2A-J. In each panel, individual blue (red) lines correspond to the spatial correlation in cadherin fluctuations near passive (active) vertices. The difference in spatial cadherin correlation between active and passive vertices in shortening junctions are shown in Figure 4—figure supplement 2A-J whereas the same data for non-shortening junctions are shown in Figure 4—figure supplement 2K-Q. By extracting the length of the spatial correlation as discussed in Section 6 above, the summary of the cadherin spatial correlation data is presented in the Main Text Figure 4G.

We used an alternative definition of C-cadherin cluster size to confirm our results. By fitting the decay in the cadherin spatial autocorrelation function to zero by an exponential function, we can extract the cluster size. We find that the asymmetry in the local cadherin clustering behavior is independent of the definition of the cluster size (Figure 4—figure supplement 1E–G). Hence, we conclude that cadherin clustering is enhanced near active vertices as opposed to passive vertices in shortening junctions (Figure 4G Main Text, Figure 4—figure supplement 1F) while it is symmetric near left and right vertices in non-shortening junctions ( Figure 4—figure supplement 1G).

Section 17. Perturbation of Cadherin clustering in individual junctions and its spatial periodicity

We calculate the spatial autocorrelation of the cadherin intensity fluctuations (Cr see Section 13,Equation (24)) for four different embryo development scenarios, (i) wild type Cdh3 Figure 4C,(ii) Cdh3 rescue (Cdh3-GFP) (see Figure 7—figure supplement 1), (iii) Cdh3 cis-mutant (cisMut-Cdh3-GFP) Figure (5D,Main Text), and (iv) Xdd1 Figure (7C,Main Text). The mean spatial correlation in cadherin fluctuations for wild type Cdh3 and Cdh3-GFP junctions show similar behavior with the decay to zero characterized by an exponential form (Figure 7—figure supplement 1B). The exponential spatial dependence is evidence for the existence of a characteristic spatial scale for correlations in cadherin spatial distribution. The local peak in the cadherin autocorrelation function is identified using the findpeaks algorithm in MATLAB. Local peak in a data array is identified when a data point is larger than its two neighboring data points or equal to infinity. The prominence of the peak is set to 0.1, identifying the peak amplitudes that stands out relative to other peaks. Wild type and rescue embryo cell-cell junctions are characterized by well-defined spatial periodicity in cadherin clustering, as observed from the secondary peaks in the spatial correlation (see black triangles, Figure 7—figure supplement 1C). Therefore, cadherin spatial organization in wild-type Cdh3 and Cdh3-cis-mutant rescue embryos is in a crystal-like phase ( Figure 7—figure supplement 1C), with regularly repeating spatial patterning. Cadherin spatial correlation for individual frames (with no averaging) is shown for control (solid lines in ; Figure 7—figure supplement 1D) and cadherin rescue embryos (dashed lines, Figure 7—figure supplement 1D). However, cadherin spatial correlation in Xdd1 and cisMut-Cdh3 embryos show diffuse spatial organization, with little to no secondary peak structures visible in the spatial autocorrelation (see Figure 7—figure supplement 1E). This is indicative of disrupted periodicity in cadherin clustering. Therefore, cadherin spatial organization in cisMut-Cdh3 and Xdd1 embryos is in a gas-like phase. Individual frame cadherin spatial correlation for cisMut-Cdh3 (solid lines Figure 7—figure supplement 1F) and Xdd1 is shown as dashed lines in Figure 7—figure supplement 1F. For Xdd1 and cisMut-Cdh3-GFP junctions, the decay in the spatial correlation is better fit by a power law, indicating the lack of existence of a coherent length scale associated with fluctuations in cadherin expression ( Figure 7—figure supplement 1G).

Section 18. Statistics

The statistical test used and other relevant details such as the number of embryos/image frames analyzed are described in the figure legends.

Data availability

Raw data from time-lapse imaging are available on Dryad.

The following data sets were generated
    1. Huebner RJ
    2. Malmi-Kakkada AN
    3. Sarıkaya S
    4. Weng S
    5. Thirumalai D
    6. Wallingford JB
    (2021) Dryad Digital Repository
    Data from:Mechanical heterogeneity along single cell-cell junctions is driven by lateral clustering of cadherins during vertebrate axis elongation.
    https://doi.org/10.5061/dryad.pg4f4qrph

References

    1. Alt S
    2. Ganguly P
    3. Salbreux G
    (2017) Vertex models: from cell mechanics to tissue morphogenesis
    Philosophical Transactions of the Royal Society B: Biological Sciences 372:20150520.
    https://doi.org/10.1098/rstb.2015.0520
    1. Fletcher AG
    2. Cooper F
    3. Baker RE
    (2017) Mechanocellular models of epithelial morphogenesis
    Philosophical Transactions of the Royal Society B: Biological Sciences 372:20150519.
    https://doi.org/10.1098/rstb.2015.0519

Decision letter

  1. Danelle Devenport
    Reviewing Editor; Princeton University, United States
  2. Kathryn Song Eng Cheah
    Senior Editor; The University of Hong Kong, Hong Kong
  3. Alpha Yap
    Reviewer; University of Queensland, Australia

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

This study provides a conceptually novel perspective on the mechanics of cell-cell junctions, and how they are regulated for morphogenetic cellular rearrangements. The cell biology of junction dynamics is a very topical subject and should be of broad interest to cell and developmental biologists interested in the mechanics of collective cell motion. It provides new biological insights combined with new theory for junctional mechanics, and is a great example of synergy between biological experiment and physics-based theory.

Decision letter after peer review:

Thank you for submitting your article "Lateral clustering of cadherins imparts mechanical heterogeneity to single cell-cell junctions during axis elongation" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Kathryn Cheah as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Α Yap (Reviewer #3).

The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.

Summary:

The authors present a detailed kinematic analysis of vertex dynamics and evaluate the role of cis-cadherin interactions in bicellular junctions during cell intercalation of Xenopus gastrulation. This is a very topical subject as there have been several papers in the past three to four years on the cell biology of junction dynamics in cell culture systems and in Drosophila models of epithelial morphogenesis. The paper provides new biological insights combined with new theory for junctional mechanics. It is a great example of synergy between biological experiment and physics-based theory.

Essential revisions:

1. The authors propose that motions of two vertices connecting shrinking junctions are independent; one vertex moves while the other remains fixed in place. It is essential that this is not a point-of reference artifact, and there are concerns about the methodology used for this analysis as the descriptions are unclear. The diagram in the supplement shows that 1 landmark is used to measure the position of the two ends of the v-junction; but a second independent point is needed for true triangulation. The second issue is that the relative positions are not measured against a fixed spatial frame but rather against local structures whose movements may be coupled to movement of the tricellular junction of interest. More details on the methodology need to be provided, and the analysis may need to be redone if indeed only 1 landmark was used.

2. A more extensive characterization of the cis-Cdh3 mutant is needed to interpret its effect on cell intercalation and vertex motion. Specifically, does the cis-Cdh3 mutant have non-junctional effects on actomyosin and cell protrusivity in a cell-autonomous manner? A cell-autonomous, non-junctional alteration in actomyosin could also lead to the observed effects on junction shrinkage and convergent extension. These data should be incorporated into a more formal hypothesis/model for the role of cis-Cdh3 interactions in vertex motion.

3. An alternative interpretation for presence of an active vertex is that it reflects the leading edge of a cell protruding mediolaterally between adjacent cells. Interestingly, another manuscript from the Wallingford lab has been posted onto BioRxiv (Weng, Huebner, and Wallingford, 2021) that includes a description of F-actin rich protrusions from the mediolateral neighbor. This neighbor protrudes, displacing the tricellular junction, and the anterior-posterior bicellular junction shrinks. Thus, the "stiff" tricellular junction, is shared by a cell with an actin-rich protrusion. This may fully explain the distinct microrheological character of the moving vertex. The authors should comment on this observation and provide a rationale for why they are not testing this hypothesis.

4. Several aspects of the methodology are missing. For instance, what criteria are used to distinguish shortening from non-shortening junctions? How are 'active' and 'passive' vertices defined? When the authors introduce their Straightness Index, it is not clear from the Results that they are talking about the straightness of motion of the vertices. There are few details about the imaging conditions, such as the z depth of the images and the time interval between frames.

5. A broadened discussion of how the findings fit (or not) into the current model of convergent extension and roles of PCP in this process is needed. Is there any known connection between the PCP machinery and Cdh3 cis-clusters? How can PCP contribute to this mechanical heterogeneity along the mediolateral axis? Additionally, further discussion of where the directionality for contraction derives from is needed. Do clustered cadherins impose a directionality to the active vertex movements?

Reviewer #1:

In follow-up to previous studies from the Wallingford group, the focus here is on junction dynamics in the anterior and posterior junctions of actively intercalating prospective notochord cells. The advances in characterizing vertex dynamics emerge from incorporating concepts from soft matter physics and microrheology. The conceptual framework borrowed from physics is an interesting move in the analysis of cell boundary motions in this classical system of directed cell rearrangement but I am not fully convinced that the framework brings new understanding to this problem. The joining of the conceptual framework of vertex analysis and the bicellular study of cis-cadherin would seek to bend principles borrowed from apical junction dynamics and apply to mesenchymal junction dynamics but it has not been made sufficiently clear what new insights this brings.

1. What exactly is "mechanical heterogeneity" and what precise role does it play in cell intercalation and convergent extension? Is it necessary, sufficient, or merely coincident with the process? Answering these questions is critical to the potential impact of this paper on the field. There are many heterogeneous events and processes throughout a single embryonic event but why is this one so important?

2. Very much like the observations from Vanderleest et al. (2018, eLife), the authors propose that motions of two vertices connecting shrinking junctions are independent; one vertex moves while the other remains fixed in place. This seems plausible but I have two issues with their analysis. The first is that the authors claim to use triangulation to track junctions in the "lab frame of reference", but I understand that triangulation requires 2 landmarks to track the absolute position of 1 point. The diagram in the supplement shows that 1 landmark is used to measure the position of the two ends of the v-junction; a second independent point is needed for true triangulation. The second issue is that the relative positions are not measured against a fixed spatial frame but rather against local structures whose movements may be coupled to movement of the tricellular junction of interest. Motions of yolk platelets or other tricellular junctions from one of the 3 cells surrounding a specific tricellular junction are likely to be mechanically coupled to that same junction. It would be prudent to use a platelet or junction from cells that are not one of these 3 cells.

3. This reviewer enjoyed the descriptive focus on vertex kinematics from the microrheological perspective, however, some background on the pro's and con's of the methodology (e.g. Crocker and Hoffman, Meth Cell Bio, 2007) would be helpful. Furthermore, the level of processing to quantify vertex fluctuations passed over several key features of vertex motion that would be of great interest to the community and should be included. For instance, it would be very helpful to describe advective kinematics of these structures starting with displacement vs. time kymographs, and extending to velocity and persistence. Are there any correlations between the active vertex and lateral (or medial) vertex motions? I understand that these vertices move in a non-uniform manner but would appreciate more intuitive description of their motion as if they were, for instance, a set of cell protrusions. A detailed "protrusion-like" analysis has not been carried out for these structures and would be useful to compare to lamellipodial kinematics and leading edge fluctuations described at the substrate level of intercalating cells.

4. This analysis suggests a novel function for tricellular junctions in mesenchymal tissues. In contrast to the tricellular junction of an epithelial sheet, this structure is not point-like but would need to be considered as a tricellular boundary that extends from the superficial, extracellular matrix facing cell surface to the most dorsal face of the notochord cell. Rather than a point, this junction is more like a knife-edge and can exhibit a complex topology typical of "escutoid cells" described by the Escudero lab (Nat Comms, 2018) or the Toyama lab (Nat Cell Bio, 2017). This raises questions about the position of the vertices measured and whether the kinematics are heterogeneous along all points of the junction, are they consistently active, or are some points advancing while others are retracting. Have the authors described kinematics of the same vertex at different z-positions?

5. Several aspects of the methodology are missing. For instance, what criteria are used to distinguish shortening from non-shortening junctions? There are few details about the imaging conditions, such as the z depth of the images and the time interval between frames.

6. The authors stress that their model is unique in driving cell intercalation but there are several theoretical and computational models have previously demonstrated the role of either mediolateral cell protrusions or anisotropic contractile bicellular junctions in directing mediolateral cell intercalation. Multiple examples of these models including recent one by Belmonte and co-workers (PLoS Comp Bio, 2016) involve heterogeneous vertices, while others not requiring heterogeneous junctions, are sufficient in driving convergent extension. The compressed exponential fits the spatial and temporal scaled kinematic changes of the shrinking bicellular junction but it is not clear whether this is simply a mechanistically-based phenomenological principle or merely a "good-fit" to the data.

7. An alternative interpretation for presence of an active vertex is that it reflects the leading edge of a cell protruding mediolaterally between adjacent cells. Why is this possibility not discussed?

8. The second half of the manuscript describes an important role for cis-cdh3 interactions in establishing or maintaining cell behaviors and polarity within converging and extending cells. The phenotypes are clearly demonstrated at the embryonic and tissue level. The subcellular phenotypes are also well described but it is not clear that the kinematic phenotypes are directly responsible for the failure of these cells to undergo directed cell rearrangement. Additionally, the cell autonomy of the defect is not clear. The authors would need to show that cis-interactions in anterior and posteriorly apposed cells alone are responsible for defects in rearrangement. For instance, would a wild-type lateral-cell, or one-lateral and one-AP cell be able to rescue polarity and active kinematics of the vertex?

9. Given the role of the actin cytoskeleton in directed cell intercalation I feel the role of cis-cdh3 interactions is only half-explored. What changes in protrusive activity, and actomyosin dynamics are perturbed? Are these specific to PCP polarity machinery operating in the mesoderm or can they also be observed in cis-cdh3 deficient non-polarized cells such as non-neural ectoderm cells (see Kim, J Cell Sci, 2011)? Up and down regulation of PCP signaling similarly regulates actomyosin contractility in both mesoderm cells and non-neural ectoderm – so this should be straightforward to test.

10. Overall, more discussion is needed about how these kinematics would fit or not fit into the current model of convergent extension and roles of PCP in this process. Is there any known connection between the PCP machinery and Cdh3 cis-clusters? How can PCP contribute to this mechanical heterogeneity along the mediolateral axis?

Reviewer #2:

The authors suggest that tricellular vertices located at opposite ends of cellular interfaces can show independent displacements, similar to what has been reported during Drosophila convergent extension movements. This is an important finding, although there are concerns about how well the analysis validates this point, as well as the brevity at which methods are explained. The study shows that these vertices demonstrate either active (directed) or passive (diffusive) movements, which, in turn, suggests that there must exist local forces that drive these specific vertex behaviors. The authors then explore what changes in the predicted cellular viscoelastic properties could be sufficient to cause vertex displacements through a mechanobiological modeling approach – these results suggest that local stiffening and relaxation of interfacial forces may be responsible for the vertex movements. To test their modeling predictions, the authors examine the distribution of cadherin proteins and observe that cadherins often cluster along cell interfaces, and that this clustering is asymmetrical at vertices that are showing "active" regimes of displacement. Finally, the authors demonstrate the cadherin clustering is regulated by PCP signaling.

There are several potentially nice findings from this study. One weakness is that the methods (especially the computational methods) are not well-described, and the findings are not detailed well in the manuscript. It is often stated that a finding supports a particular hypothesis, followed by a reference to a figure, but there is not a detailed description of what the findings actually are and how this specifically supports the hypothesis. At times, this makes the manuscript read superficially. I believe the Results section needs substantial re-writing to more adequately explain the computational sections (~first half of manuscript). The Discussion is also brief in content. More specific comments follow below:

1. I thought the authors had a bit of an odd way of introducing the work, especially the paragraph suggesting "a similarly granular understanding of subcellular mechanical properties" has not been achieved. (From Intro, "For example, the localization and turnover of actomyosin and cadherin adhesion proteins have been extensively quantified during Drosophila CE (Blankenship et al., 2006; Fernandez-Gonzalez et al., 2009; Levayer and Lecuit, 2013; Rauzi et al., 2008)), as have similar patterns for the Planar Cell Polarity (PCP) proteins and actomyosin during vertebrate CE (Butler and Wallingford, 2018; Kim and Davidson, 2011; Shindo and Wallingford, 2014). However, the significance of these molecular patterns remains unclear because we lack a similarly granular understanding of subcellular mechanical properties and their dynamics, which ultimately explain the cell behaviors that drive CE.".

I think the authors have a potentially interesting study, but it does not appear to address a significantly different scale than what many studies out of the Lecuit lab (or others) have addressed (e.g., Fernandez-Gonzalez, Gardel, Campos, Dahmann, Kiehart, or Hutson labs). It would be appropriate to better acknowledge prior work – it does not detract from the accomplishments of this study. My apologies, but at times the writing, especially the physical overlay of the paper, sounds dismissive of other works.

2. It is not always clear how some of the biophysical analysis are performed and/or support the authors major contentions. One example, "We found that v-junction shortening was dominated by the movement of a single "active" vertex, while the other "passive" vertex moved comparatively less (Figure 1C, D)(SI, Section 1). Three distinct metrics demonstrated that this asymmetry was not a point-of-reference artifact (Supp. Figure 2)."

While I suspect they are correct, this is one major sticking point and it appears the authors are not meeting scientific standard in demonstrating this point in its current form. First, the wording 'Three distinct metrics demonstrated that this asymmetry was not a point-of-reference artifact' seems to suggest that the authors are showing three independent pieces of evidence, but this is not the case (maybe this impression was not intended, so maybe reword?). What the authors are actually showing are the MSD results in three different coordinate systems (the 'lab' frame, the 'cell' frame which is a reference frame relative to a yolk particle, and the reference frame relative to a non-moving neighboring vertex). As best as I can guess, this is the comparison of the results from the three reference frames that would (potentially) allow the conclusion that the different motion in the two vertices is not an artifact, but this is not possible to tell, because the authors only describe their results in the supplementary figure, and do not explain anywhere how/why these three different results prove the point that the different motion cannot be a reference point artifact. The mere fact that the authors were able to identify three different reference frames in which the vertices move differently does not meet this threshold; they would have to explain better why one of them (e.g. the cell frame) represents something like a fixed local coordinate system, and – for example – show that an ensemble of yolk particles doesn't 'deform' significantly over the associated time scales (for example, they could show that the yolk particles only minimally changes their interparticle distances during this time?).

Additionally, the authors write in the figure legend 'We refer to this as the relative MSD in the "cell" frame of reference, which eliminates the effect of translational and rotational motion of the tissue during time-lapse imaging.' What the authors show in the figure is a single yolk particle as reference point, and a single reference point would only be able to eliminate the effect of translation, but not translation and rotation at the same time. So are the authors using only a single yolk particle for a set of two vertices and ignoring rotation effects? Or are they using a system where they can construct a coordinate system from multiple yolk particles simultaneously (which could correct for both translation and rotation) but not showing this procedure in the figure? And going forward, which reference frame are the authors using for their analyses, since all three show different results, and why? These things would be best explained explicitly in a section of the supplement.

3. Where does the directionality for contraction derive from? I found the authors "transverse" vs "in-line" coordinate system somewhat confusing. Transverse in other studies has often been applied to the non-contracting interface, but lines drawn in figure schematics seem to indicate a more cell-center axis. I believe the authors are showing more clustered, stable adhesions correlating with "active" vertices, but does this impose a directionality to the active vertex movements (in the experimental data sets)? Any further description would be helpful, and this could also be expanded on in the Discussion.

4. Some of the MSD difference between active and passive vertices appear small. It is not clear how we know that the differences between active and passive vertices represent something 'real' and not an artifact of the classification process. In the first section of the results, the authors are comparing various metrics (such as MSD) between 'active' and 'passive' vertices, but I am not finding a single clear explanation of how these categories were defined. Are the authors using a threshold to classify a given vertex as active or passive? Or are the authors taking vertex pairs, and splitting up each pair into one active and one passive partner, based on MSD magnitude? This is a critical piece of information for interpreting the results. Can the authors show that there are two 'modes' of behavior (active and passive) using a clustering approach of some type?

5. I would like to hear more interpretation of what the mechanical properties of the cells are that are being affected in the -cis binding mutants (this is taken somewhat as canon, but does it behave the same in these Xenopus explants?). I know the authors say cell-cell adhesion is (somewhat?) rescued by this -cis mutant and embryos do not fully dissociate. Can the authors better detail the degree to which the strength of cell-cell adhesion is rescued versus local properties like the asymmetry of adhesive forces at cell vertices?

6. A final note about the modeling. About their model predictions, the authors state that 'Our theory makes a curiously counter-intuitive prediction: that the more fluid-like motion of the active vertex occurs in the context of increased local stiffness (i.e. higher viscoelastic parameter), while the more glass-like motion of the passive vertex occurs in a relatively decreased stiffness regime.'

I am not sure that there is something counter-intuitive about this finding. While it is true that in the classic model for epithelial morphology (Farhadifar et al. 2007), the more fluid-like behavior is associated with lower stiffness, that's because it's related to adhesion forces dominating over elastic forces, so the asymmetric vertex movement is being driven by the minimization of adhesion energies. In the authors' model, there are no adhesion forces, and the vertex displacement is driven by the external piston forces – so it seems logical that the more effective motion (in the active vertex) would occur in the case where the higher spring stiffness allows better force transmission (and the passive vertex is the one where the forces dissipates more quickly in the softer environment). Thus, the fluidization arguments from other models/systems in the literature would not seem to fully apply to this system.

7. "Symmetrical clustering in non-shortening reflects the symmetrical dynamics of vertices bounding these junctions" – I believe "reflects" suggests a direct connection, whereas this is more of a "correlates" or "suggestive" statement.

8. Figures often have panel titles like "Deviation from compressed exponential" – it would helpful to better title these to indicate the rough property that the authors are trying to report on, and put more specificity into the figure legends.

Reviewer #3:

I think that this is an interesting and important report, for the following reasons. (1) It introduces the concept that cell-cell adherens junctions are mechanically heterogeneous and this mechanical asymmetry mediates the changes in junctional length that underlie convergent extension. And it introduces interesting new theory that incorporates this concept. (2) The authors provide a biological function for cadherin clustering, something which has not been available to date. Importantly, their explanation bridges scales, i.e. they show that clustering (a molecular event) contributes to convergence extension by modulating junctional mechanics (a cellular biophysical parameter). In general, the data are of excellent quality and the study represents an exemplary case of synergy between experiment and theory.

I suspect that this study is not the end of the matter. In particular, it would be important to understand how local differences in cadherins affect junctional mechanics. The authors cite earlier work from the Mege lab indicating that cadherins can influence membrane mechanics. Whether this is at the level of the bilayer or via alterations in the cortical cytoskeleton would be important to address. But this is beyond the reasonable scope of a paper; indeed, it would speak to the potential for this study to motivate future research.

1. Figure 4G. Is this correct as currently presented? The authors describe this as showing that cadherin cluster size near non-shortening vertices is the same as that around the passive vertices in shortening junctions. But to my eye, what is drawn as the non-shortening data set looks similar to the set that is labelled as (active). Has something been mislabelled?

2. Embryo cohesion. This is measured as embryo survival at stage 23. But that seems to me to be a very indirect measure of tissue integrity. Changes in survival may reflect catastrophic loss of integrity, but miss more subtle features. I would be happy enough if they were to use the term "viability" instead of "cohesion". There is still a very interesting different in effect of the cis-mutant.

3. I think that some of the analyses could be explained more intuitively for the general reader. For example, when the authors introduce their Straightness Index, it is not clear from the Results that they are talking about the straightness of motion of the vertices. (For junction folks, "straightness" sounds like the measures of junctional straightness that have been used as proxies of line tension.) It would only take a sentence to give an intuitive explanation in this and other instances.

(By the way, the text and caption to Figure 3 give the reference for the Straightness Index as SI Section 14, but I think that it is actually Section 16.)

4. Glass-like behaviour in junctions. To what extent can one really say that the passive junctions are "more glass-like". If I read Figure 1E correctly, the exponent of "t" for the passive junctions is still >1 (1.3 from Figure 1E). So, is it more helpful to simply regard them as less fluidized, rather than invoking subdiffusive behaviour (which would require the exponent to be <1)? I'm happy to the corrected by the authors (or the other reviewers), but beyond a point of phenomenology I'm still not sure that I can see an underlying intuition that would be really helpful.

Along these lines, is it possible to statistically compare the differences in the exponentials?

5. "Non-shortening" junctions. Were these tested away from junctions that shortened? What about the junctions that also contribute to the vertices at the ends of the junctions that shortened? Did these show any asymmetry in mechanics or in cadherin clustering?

https://doi.org/10.7554/eLife.65390.sa1

Author response

Essential revisions:

1. The authors propose that motions of two vertices connecting shrinking junctions are independent; one vertex moves while the other remains fixed in place. It is essential that this is not a point-of reference artifact, and there are concerns about the methodology used for this analysis as the descriptions are unclear. The diagram in the supplement shows that 1 landmark is used to measure the position of the two ends of the v-junction; but a second independent point is needed for true triangulation. The second issue is that the relative positions are not measured against a fixed spatial frame but rather against local structures whose movements may be coupled to movement of the tricellular junction of interest. More details on the methodology need to be provided, and the analysis may need to be redone if indeed only 1 landmark was used.

We agree that it is essential to show vertex movements are not a point-of-reference artifact. We regret, therefore, that the original manuscript was not sufficiently clear on this point. In fact, what we call the “lab frame of reference” provides the “fixed spatial frame” the reviewers were concerned was missing.

As now clarified with a new schematic in the revised Figure 1—figure supplement 2, the “lab frame of reference” is a fixed coordinate system, where we used the pixels of the image to establish the coordinates with the upper left pixel set at (x,y)(0,0). This fixed lab frame of reference was used to generate the data in Figure1 and in Figure 1—figure supplement 1. These new points are discussed on page 4 of the revision.

Accordingly, the measures made using internal landmarks (yolk platelet, neighboring vertex) are secondary to our measurements using the fixed coordinate system. Nonetheless, we feel these are important to address the potential artifacts that might be introduced into our fixed frame quantification by overall tissue drift in the microscope. Thus, we further strengthened these secondary analyses by adding MSD plots for the yolk particles and the nearby vertices used as landmarks in Figure 1—figure supplement 2 (see panels E and G) showing that these landmarks move less compared to the vertices. We clarified this issue on page 4 of the manuscript.

Finally, to avoid confusion, we have removed the word “triangulation” from the figure legend.

2. A more extensive characterization of the cis-Cdh3 mutant is needed to interpret its effect on cell intercalation and vertex motion. Specifically, does the cis-Cdh3 mutant have non-junctional effects on actomyosin and cell protrusivity in a cell-autonomous manner? A cell-autonomous, non-junctional alteration in actomyosin could also lead to the observed effects on junction shrinkage and convergent extension. These data should be incorporated into a more formal hypothesis/model for the role of cis-Cdh3 interactions in vertex motion.

A more thorough characterization of the cis-Cdh3 mutant will undoubtably provide exciting results, but we respectfully argue that such work is beyond the scope of the present paper, for reasons both philosophical and practical:

Philosophically, we would argue that a deeper dive into Cadherin function will not enhance the results of this manuscript. Our results that Cdh3 clustering is required for an essential developmental process represent a significant step, as this has not been shown previously in the context of any intact animal. Moreover, we link clustering to the normal execution of novel mechanical behaviors that we also report here for the first time, providing a mechanistic link between subcellular mechanics, cadherin clustering and an embryonic phenotype. Finally, we link these biological phenotypes to fundamental physical attributes that we also report here for the first time. Thus, we feel that further dissection of any single aspect of this paper (e.g. clustering) would actually distract the reader from what is already a lengthy story arc. We hope the reviewers and the Editor can be convinced to agree!

From a practical standpoint, we note as well that testing cell autonomy of our cisMut-Cdh3 reagents in vivo is perhaps less straightforward than it seems: The experiment would require examining mosaics, and to generate these, we would inject single blastomeres at late cleavage stages and rely on CE-mediated cell mixing to place control cells next to experimental cells. However, since cisMUT-Cdh3 blocks intercalation, no cell mixing will occur, precluding accurate assessment of cell autonomy. At the very best, we may be able to image cell behaviors at the edge of a clone, a half-measure by any measure. We are currently exploring optogenetic approaches by which we may explore this important issue, but we feel those experiments are far beyond the scope of the present work.

3. An alternative interpretation for presence of an active vertex is that it reflects the leading edge of a cell protruding mediolaterally between adjacent cells. Interestingly, another manuscript from the Wallingford lab has been posted onto BioRxiv (Weng, Huebner, and Wallingford, 2021) that includes a description of F-actin rich protrusions from the mediolateral neighbor. This neighbor protrudes, displacing the tricellular junction, and the anterior-posterior bicellular junction shrinks. Thus, the "stiff" tricellular junction, is shared by a cell with an actin-rich protrusion. This may fully explain the distinct microrheological character of the moving vertex. The authors should comment on this observation and provide a rationale for why they are not testing this hypothesis.

This is a very important point, and we regret not addressing it in the original manuscript. In truth, the paper was so lengthy already that we sought to simplify it by not discussing actin. We see now that this was a mistake. We therefore have now added data that address this issue.

We quantified actin intensity in the regions of shortening v-junctions near active and passive vertices. As we now show in Figure 4—figure supplement 1, we observed no asymmetry in this region (which is the same region in which we observed asymmetry of cadherin clustering). These data, presented on page 7 of the revision, argue against the simple explanation that active and passive vertices are the result of asymmetric protrusive activity and cell crawling.

In addition, we note that the reviewers’ statement above concerning the data in our preprint from Weng et al. is in fact not accurate. The review states: “This neighbor protrudes, displacing the tricellular junction….” But this is not what we reported. Rather, those experiments were carefully designed to identify tricellular junctions using a membrane marker independently of the actin signal used to observe protrusions. This approach allowed us to observe that in some cases protrusion-related actin assembly is associated with vertex motion, but in an equal number of cases, it clearly is not. Thus, there is not a simple relationship between actin-rich protrusions and the active or passive vertex. We believe that a careful look at the data in Figure 2, Figure 1—figure supplement 2 and Supp. Figure 4 of the Weng et al. preprint should make this point clear.

Thus, while the reviewers are correct that understanding the relationship between actin and vertex motion will be critical, that relationship is quite complex. Thus, we hope that the new data in Figure 2—figure supplement 1 of the revised manuscript will suffice in the context of this paper.

4. Several aspects of the methodology are missing. For instance, what criteria are used to distinguish shortening from non-shortening junctions? How are 'active' and 'passive' vertices defined? When the authors introduce their Straightness Index, it is not clear from the Results that they are talking about the straightness of motion of the vertices. There are few details about the imaging conditions, such as the z depth of the images and the time interval between frames.

We wish to apologize to the reviewers here, as we realize now that much of the original supplemental information (appendix) was incorrectly organized, so that many relevant sections were not called out properly in the main manuscript. As a result, the manuscript appeared to be lacking methodological details.

To correct these mistakes, we have reorganized the Appendix, updated the Appendix callouts in the main manuscript, updated the experimental methods section, and added text to the main manuscript to clarify our methodology. Details for each specific point are below.

1. Criteria for distinguishing shortening vs non-shortening junctions. Any junction not shortening over a 400s timescale was considered non-shortening. We have added this criterion for junction shortening to the main text (pg.5) as well as a callout to the Appendix (section 1).

2. Definition of ‘active’ and ‘passive’ vertices. The quantitative definition of the active and passive vertex is also given in the Appendix (section 1). To clarify this point, we have added a brief description of the method used to define the active and passive vertex to the main manuscript (pg.4) as well as a callout to SI Section 1, as follows:

3. Definition of Straightness Index. Our Straightness Index is defined in detail in the Appendix Section 12 and refers to vertex motion and not bicellular junction “straightness”. To clarify this point, we added the following text to the main manuscript (pg.6), as well as a callout to SI Section 12.

4. Missing details of imaging conditions. We have updated the experimental methods to include these missing methods (pg.13) and have also included the imaging conditions the figure legend for Figure 1B (pg.10).

5. A broadened discussion of how the findings fit (or not) into the current model of convergent extension and roles of PCP in this process is needed. Is there any known connection between the PCP machinery and Cdh3 cis-clusters? How can PCP contribute to this mechanical heterogeneity along the mediolateral axis? Additionally, further discussion of where the directionality for contraction derives from is needed. Do clustered cadherins impose a directionality to the active vertex movements?

We have substantially revised the Discussion to include a more thorough treatment of these issues.

Reviewer #1:

In follow-up to previous studies from the Wallingford group, the focus here is on junction dynamics in the anterior and posterior junctions of actively intercalating prospective notochord cells. The advances in characterizing vertex dynamics emerge from incorporating concepts from soft matter physics and microrheology. The conceptual framework borrowed from physics is an interesting move in the analysis of cell boundary motions in this classical system of directed cell rearrangement but I am not fully convinced that the framework brings new understanding to this problem. The joining of the conceptual framework of vertex analysis and the bicellular study of cis-cadherin would seek to bend principles borrowed from apical junction dynamics and apply to mesenchymal junction dynamics but it has not been made sufficiently clear what new insights this brings.

1. What exactly is "mechanical heterogeneity" and what precise role does it play in cell intercalation and convergent extension? Is it necessary, sufficient, or merely coincident with the process? Answering these questions is critical to the potential impact of this paper on the field. There are many heterogeneous events and processes throughout a single embryonic event but why is this one so important?

Mechanical heterogeneity in this context refers to the differences in mechanical properties along a single cell-cell junction. It is true that Vanderleest et al. (2018, eLife), reported asymmetry and physical independence in the movement of two vertices bounding a single cell-cell junction. We nonetheless feel our manuscript is the first to directly demonstrate mechanical heterogeneity along the junction linking these two vertices.

Indeed, this novelty is significant enough that it has drawn the attention of the Gardel lab, leaders in the field. They have now posted a preprint in the BioRxiv reporting their own novel theoretical model to address the very mechanical heterogeneity along junctions that we describe here (https://www.biorxiv.org/content/10.1101/2021.02.26.433093v1). Critically, the work in that preprint uses optogenetics and cell culture, so provides an interesting complement to the in vivo work we present here.

Finally, and perhaps most crucially, we not only show that this heterogeneity exists in a developing vertebrate animal in vivo, but also that this heterogeneity is necessary for convergent extension and requires the function Cdh3 and PCP signaling.

We have expanded the Intro and Discussion of the paper to better emphasize this important point.

2. Very much like the observations from Vanderleest et al. (2018, eLife), the authors propose that motions of two vertices connecting shrinking junctions are independent; one vertex moves while the other remains fixed in place. This seems plausible but I have two issues with their analysis. The first is that the authors claim to use triangulation to track junctions in the "lab frame of reference", but I understand that triangulation requires 2 landmarks to track the absolute position of 1 point. The diagram in the supplement shows that 1 landmark is used to measure the position of the two ends of the v-junction; a second independent point is needed for true triangulation. The second issue is that the relative positions are not measured against a fixed spatial frame but rather against local structures whose movements may be coupled to movement of the tricellular junction of interest. Motions of yolk platelets or other tricellular junctions from one of the 3 cells surrounding a specific tricellular junction are likely to be mechanically coupled to that same junction. It would be prudent to use a platelet or junction from cells that are not one of these 3 cells.

The reviewer is correct about use of the word triangulation, and we have removed the term from the manuscript. We did however measure the MSD from three principally independent frames of reference. The first is a fixed coordinate system (lab frame of reference) where we used the pixels of the image to establish the coordinates with the upper left pixel set at (x,y)(0,0). The fixed lab frame of reference was used for the data in figure1 and Figure 1—figure supplement 2. In addition, we used two additional non-fixed landmarks to measure the MSD. Here we used yolk particles within the intercalating cell and neighboring vertices as the reference frame. As we observe similar MSD from each of these coordinate systems, one fixed and two internal landmarks, we confident in reporting our MSD results. These points have been clarified in the revision.

3. This reviewer enjoyed the descriptive focus on vertex kinematics from the microrheological perspective, however, some background on the pro's and con's of the methodology (e.g. Crocker and Hoffman, Meth Cell Bio, 2007) would be helpful. Furthermore, the level of processing to quantify vertex fluctuations passed over several key features of vertex motion that would be of great interest to the community and should be included. For instance, it would be very helpful to describe advective kinematics of these structures starting with displacement vs. time kymographs, and extending to velocity and persistence. Are there any correlations between the active vertex and lateral (or medial) vertex motions? I understand that these vertices move in a non-uniform manner but would appreciate more intuitive description of their motion as if they were, for instance, a set of cell protrusions. A detailed "protrusion-like" analysis has not been carried out for these structures and would be useful to compare to lamellipodial kinematics and leading edge fluctuations described at the substrate level of intercalating cells.

We agree this is an important issue. We note that persistence of motion is, in fact addressed in Figure 3E, F and that our newest efforts to understand protrusive activity are reported in our new preprint from Went et al.

4. This analysis suggests a novel function for tricellular junctions in mesenchymal tissues. In contrast to the tricellular junction of an epithelial sheet, this structure is not point-like but would need to be considered as a tricellular boundary that extends from the superficial, extracellular matrix facing cell surface to the most dorsal face of the notochord cell. Rather than a point, this junction is more like a knife-edge and can exhibit a complex topology typical of "escutoid cells" described by the Escudero lab (Nat Comms, 2018) or the Toyama lab (Nat Cell Bio, 2017). This raises questions about the position of the vertices measured and whether the kinematics are heterogeneous along all points of the junction, are they consistently active, or are some points advancing while others are retracting. Have the authors described kinematics of the same vertex at different z-positions?

We fully agree that an analysis of cell-cell junction mechanics along the length of the z-axes would be very informative, but we are limited both experimentally and within the scope of this single manuscript. The mesenchymal bi-cellular junctions and tricellular junctions do change depending on z-position, as is likely true with epithelial tissues, but we are limited by the time in which our microscopes can acquire t and z-stacks. The analysis in this manuscript required high temporal resolution which unfortunately prevented the acquisition of multiple z-positions. Also, while we take a bit of a reductionist approach looking at a single z-plane in this manuscript, we believe that this simplification of the biological problem allowed the detailed analysis of vertex movements which comprises the first half of the paper. An analysis of vertex movements at different z-positions will be an exciting future direction.

5. Several aspects of the methodology are missing. For instance, what criteria are used to distinguish shortening from non-shortening junctions? There are few details about the imaging conditions, such as the z depth of the images and the time interval between frames.

We apologize to the reviewer as some of the methodology was either missing or incorrectly ordered in the theory supplemental information (SI). We have added the missing methodology and reorganized the Appendix to correctly match the main manuscript

Specifically:

1. Criteria for distinguishing shortening vs non-shortening junctions. Any junction not shortening over a 400s timescale was considered non-shortening. We have added this criterion for junction shortening to the main text (pg.5) and to the Appendix (section 1).

2. Missing details of imaging conditions. We have updated the experimental methods to include these missing methods (pg.13) and have also included the imaging conditions the figure legend for Figure 1B (pg.10).

“Frames were acquired at a z-depth of 5μm above the ECM/coverslip and with a time interval of 2 seconds”

6. The authors stress that their model is unique in driving cell intercalation but there are several theoretical and computational models have previously demonstrated the role of either mediolateral cell protrusions or anisotropic contractile bicellular junctions in directing mediolateral cell intercalation. Multiple examples of these models including recent one by Belmonte and co-workers (PLoS Comp Bio, 2016) involve heterogeneous vertices, while others not requiring heterogeneous junctions, are sufficient in driving convergent extension. The compressed exponential fits the spatial and temporal scaled kinematic changes of the shrinking bicellular junction but it is not clear whether this is simply a mechanistically-based phenomenological principle or merely a "good-fit" to the data.

There are indeed many models of CE and we feel that all have value. However, the paper from Belmonte seeks to model purely filipodia-driven cell crawling. Work from the Sutherland and Toyama Labs, as well as our recent work in BioRxiv from Weng et al., show that CE in diverse animals is driven by an integration of cell crawling and junction contraction. It is thus that we specifically designed a model of vertex motion that was agnostic concerning the cell biological basis, and instead modeled simply the local mechanical environment. Just the same, we think this point deserve attention, and we have now included a discussion of the Belmonte model in the revision.

7. An alternative interpretation for presence of an active vertex is that it reflects the leading edge of a cell protruding mediolaterally between adjacent cells. Why is this possibility not discussed?

The interpretation that the active vertex is the protruding leading edge of a mediolateral cell was actually our first hypothesis prior to quantitatively analyzing the data. In fact, we collect a large dataset of time-lapse videos of actin at shortening v-junctions but when we analyzed this data, we found no correlation between actin accumulation, active/passive vertices, and junction shortening. We have included a new supplemental figure (2E-G) showing that actin at the active or passive vertex does not correlate with junction shortening. This issue is also addressed in more detail in the BioRxiv preprint by Weng et al.

8. The second half of the manuscript describes an important role for cis-cdh3 interactions in establishing or maintaining cell behaviors and polarity within converging and extending cells. The phenotypes are clearly demonstrated at the embryonic and tissue level. The subcellular phenotypes are also well described but it is not clear that the kinematic phenotypes are directly responsible for the failure of these cells to undergo directed cell rearrangement. Additionally, the cell autonomy of the defect is not clear. The authors would need to show that cis-interactions in anterior and posteriorly apposed cells alone are responsible for defects in rearrangement. For instance, would a wild-type lateral-cell, or one-lateral and one-AP cell be able to rescue polarity and active kinematics of the vertex?

As explained in more detail in our response to the essential revisions, above, we feel that a further exploration of Cdh3 function is beyond the scope of this already rather large paper.

9. Given the role of the actin cytoskeleton in directed cell intercalation I feel the role of cis-cdh3 interactions is only half-explored. What changes in protrusive activity, and actomyosin dynamics are perturbed? Are these specific to PCP polarity machinery operating in the mesoderm or can they also be observed in cis-cdh3 deficient non-polarized cells such as non-neural ectoderm cells (see Kim, J Cell Sci, 2011)? Up and down regulation of PCP signaling similarly regulates actomyosin contractility in both mesoderm cells and non-neural ectoderm – so this should be straightforward to test.

These are all outstanding questions, and we are excited to explore them. However, by endeavoring to make parallel contributions in both cell biology and physics, we have generated 50 panels of data in the main figures alone, and more than 30 additional panels of data in the supplement. Thus, straightforward or not, we feel that additional consideration of the cell biology here is beyond the scope of the current work.

10. Overall, more discussion is needed about how these kinematics would fit or not fit into the current model of convergent extension and roles of PCP in this process. Is there any known connection between the PCP machinery and Cdh3 cis-clusters? How can PCP contribute to this mechanical heterogeneity along the mediolateral axis?

We have now provided additional treatment of these points in the Discussion section of the manuscript.

Reviewer #2:

[…] There are several potentially nice findings from this study. One weakness is that the methods (especially the computational methods) are not well-described, and the findings are not detailed well in the manuscript. It is often stated that a finding supports a particular hypothesis, followed by a reference to a figure, but there is not a detailed description of what the findings actually are and how this specifically supports the hypothesis. At times, this makes the manuscript read superficially. I believe the Results section needs substantial re-writing to more adequately explain the computational sections (~first half of manuscript). The Discussion is also brief in content. More specific comments follow below:

1. I thought the authors had a bit of an odd way of introducing the work, especially the paragraph suggesting "a similarly granular understanding of subcellular mechanical properties" has not been achieved. (From Intro, "For example, the localization and turnover of actomyosin and cadherin adhesion proteins have been extensively quantified during Drosophila CE (Blankenship et al., 2006; Fernandez-Gonzalez et al., 2009; Levayer and Lecuit, 2013; Rauzi et al., 2008)), as have similar patterns for the Planar Cell Polarity (PCP) proteins and actomyosin during vertebrate CE (Butler and Wallingford, 2018; Kim and Davidson, 2011; Shindo and Wallingford, 2014). However, the significance of these molecular patterns remains unclear because we lack a similarly granular understanding of subcellular mechanical properties and their dynamics, which ultimately explain the cell behaviors that drive CE.".

I think the authors have a potentially interesting study, but it does not appear to address a significantly different scale than what many studies out of the Lecuit lab (or others) have addressed (e.g., Fernandez-Gonzalez, Gardel, Campos, Dahmann, Kiehart, or Hutson labs).

We respectfully dispute this assertion. While from the standpoint of basic physics the scales are similar, there are several biological distinctions that make our work both novel and highly significant:

1. Of the six labs mentioned above, five work exclusively with Drosophila and the sixth with cultured epithelial cells. A broader exploration of the issue in other settings, such as the vertebrate animal Xenopus, is critical so that we may learn which elements of Drosophila CE are universal and which, like the fly itself, are evolutionarily derived.

2. Moreover, all of the work referenced above deals only with well-behaved polarized epithelial cells, while our work is the messier context of mesenchymal cells. We think our extension from one tissue type to another is cell biologically very important. This is especially significant, because we did not expect the mesenchymal cells that we studied to share so many features with previously studied epithelial cells!

3. Perhaps most critically, neither Drosophila nor cultured cells rely on PCP signaling for CE, yet PCP signaling is essential for both mesenchymal and epithelial CE in all vertebrate embryos, as well as in several vertebrate organ systems. Thus, PCP-mediated CE is an essential biological process that cannot be studied in Drosophila or in cultured cells, making our new findings in Xenopus highly significant.

4. Finally, human birth defects are the most lethal diseases of children in the US (twice as lethal as pediatric cancers) and PCP genes are among the most well-defined genetic risk factors for human neural tube defects. Thus, understanding the biomechanics and cell biology specifically of PCP-dependent CE, which again cannot be explored in flies of cell culture, is highly significant.

It would be appropriate to better acknowledge prior work – it does not detract from the accomplishments of this study. My apologies, but at times the writing, especially the physical overlay of the paper, sounds dismissive of other works.

We are very sensitive to this concern. We have now added substantially more verbiage and several additional citations, both in the Introduction and in the Discussion, in an effort to address it.

2. It is not always clear how some of the biophysical analysis are performed and/or support the authors major contentions. One example, "We found that v-junction shortening was dominated by the movement of a single "active" vertex, while the other "passive" vertex moved comparatively less (Figure 1C, D)(SI, Section 1). Three distinct metrics demonstrated that this asymmetry was not a point-of-reference artifact (Supp. Figure 2)."

While I suspect they are correct, this is one major sticking point and it appears the authors are not meeting scientific standard in demonstrating this point in its current form. First, the wording 'Three distinct metrics demonstrated that this asymmetry was not a point-of-reference artifact' seems to suggest that the authors are showing three independent pieces of evidence, but this is not the case (maybe this impression was not intended, so maybe reword?). What the authors are actually showing are the MSD results in three different coordinate systems (the 'lab' frame, the 'cell' frame which is a reference frame relative to a yolk particle, and the reference frame relative to a non-moving neighboring vertex). As best as I can guess, this is the comparison of the results from the three reference frames that would (potentially) allow the conclusion that the different motion in the two vertices is not an artifact, but this is not possible to tell, because the authors only describe their results in the supplementary figure, and do not explain anywhere how/why these three different results prove the point that the different motion cannot be a reference point artifact. The mere fact that the authors were able to identify three different reference frames in which the vertices move differently does not meet this threshold; they would have to explain better why one of them (e.g. the cell frame) represents something like a fixed local coordinate system, and – for example – show that an ensemble of yolk particles doesn't 'deform' significantly over the associated time scales (for example, they could show that the yolk particles only minimally changes their interparticle distances during this time?).

Additionally, the authors write in the figure legend 'We refer to this as the relative MSD in the "cell" frame of reference, which eliminates the effect of translational and rotational motion of the tissue during time-lapse imaging.' What the authors show in the figure is a single yolk particle as reference point, and a single reference point would only be able to eliminate the effect of translation, but not translation and rotation at the same time. So are the authors using only a single yolk particle for a set of two vertices and ignoring rotation effects? Or are they using a system where they can construct a coordinate system from multiple yolk particles simultaneously (which could correct for both translation and rotation) but not showing this procedure in the figure? And going forward, which reference frame are the authors using for their analyses, since all three show different results, and why? These things would be best explained explicitly in a section of the supplement.

These are crucial points. As discussed in detail in response to a similar comment, above, this concern stems from a lack of clarity in our initial submission. A new schematic in Figure 1—figure supplement 2 clarifies that we used a fixed frame of reference and a coordinate system for the key measurements in Figure 1. We also included the MSD for the yolk particle and the neighboring vertex Figure 1—figure supplement 2, compared to the fixed reference frame, to show minimal movement of these structures compared to the vertices. Finally, we removed language concerning “triangulation” and “translation and rotation of motion” as they were incorrectly used. Instead, we have clarified that we measured the MSD from three principally independent frames of reference, one fixed and two that are local within the image.

3. Where does the directionality for contraction derive from? I found the authors "transverse" vs "in-line" coordinate system somewhat confusing. Transverse in other studies has often been applied to the non-contracting interface, but lines drawn in figure schematics seem to indicate a more cell-center axis. I believe the authors are showing more clustered, stable adhesions correlating with "active" vertices, but does this impose a directionality to the active vertex movements (in the experimental data sets)? Any further description would be helpful, and this could also be expanded on in the Discussion.

We have made an effort to address this complex issue in the revised discussion, though we note that full understanding is still a long way off!

Also, we do note that transverse in our context is different from that used in Drosophila where transverse junctions (t-junctions) are those perpendicular to the shortening vertical junctions (v-junctions). We have maintained the use of t,v-junctions to be consistent with work done in Drosophila but do appreciate that this may add to some confusion. Here we used transverse fluctuations to describe vertex motion that is perpendicular to the shortening junction. We have added text to main manuscript (pg.6) to help clarify our use of the term transverse. The theory appendix (section 12) also provides a more thorough quantitative description of transverse fluctuations which we hope clarifies this point.

4. Some of the MSD difference between active and passive vertices appear small. It is not clear how we know that the differences between active and passive vertices represent something 'real' and not an artifact of the classification process. In the first section of the results, the authors are comparing various metrics (such as MSD) between 'active' and 'passive' vertices, but I am not finding a single clear explanation of how these categories were defined. Are the authors using a threshold to classify a given vertex as active or passive? Or are the authors taking vertex pairs, and splitting up each pair into one active and one passive partner, based on MSD magnitude? This is a critical piece of information for interpreting the results. Can the authors show that there are two 'modes' of behavior (active and passive) using a clustering approach of some type?

The classification method for the active and passive vertex is defined in the theory appendix section 1. As noted above, our initial submission had some organizational errors the theory appendix which have been fixed for the resubmission. We apologize and ask reviewers to please see the updated theory appendix. We also appreciate that defining the active and passive vertex is a key element of this manuscript and have updated the main manuscript with this definition (pg.4).

5. I would like to hear more interpretation of what the mechanical properties of the cells are that are being affected in the -cis binding mutants (this is taken somewhat as canon, but does it behave the same in these Xenopus explants?). I know the authors say cell-cell adhesion is (somewhat?) rescued by this -cis mutant and embryos do not fully dissociate. Can the authors better detail the degree to which the strength of cell-cell adhesion is rescued versus local properties like the asymmetry of adhesive forces at cell vertices?

We feel that these questions, while important, are beyond the scope of the already large paper here.

6. A final note about the modeling. About their model predictions, the authors state that 'Our theory makes a curiously counter-intuitive prediction: that the more fluid-like motion of the active vertex occurs in the context of increased local stiffness (i.e. higher viscoelastic parameter), while the more glass-like motion of the passive vertex occurs in a relatively decreased stiffness regime.'

I am not sure that there is something counter-intuitive about this finding. While it is true that in the classic model for epithelial morphology (Farhadifar et al. 2007), the more fluid-like behavior is associated with lower stiffness, that's because it's related to adhesion forces dominating over elastic forces, so the asymmetric vertex movement is being driven by the minimization of adhesion energies. In the authors' model, there are no adhesion forces, and the vertex displacement is driven by the external piston forces – so it seems logical that the more effective motion (in the active vertex) would occur in the case where the higher spring stiffness allows better force transmission (and the passive vertex is the one where the forces dissipates more quickly in the softer environment). Thus, the fluidization arguments from other models/systems in the literature would not seem to fully apply to this system.

We understand this sentiment, but after several presentations, we are acutely aware that this result is in fact quite counter-intuitive to cell biology audiences! Just the same, we have removed the term counter-intuitive from the main manuscript.

7. "Symmetrical clustering in non-shortening reflects the symmetrical dynamics of vertices bounding these junctions" – I believe "reflects" suggests a direct connection, whereas this is more of a "correlates" or "suggestive" statement.

8. Figures often have panel titles like "Deviation from compressed exponential" – it would helpful to better title these to indicate the rough property that the authors are trying to report on, and put more specificity into the figure legends.

We appreciate this comment and have spent a significant amount of time trying to create useful titles that satisfy both the physicists and biologists. We settled on titles that use the same language as the theory appendix where we define most of the graphs. Our hope is that the theory appendix can clarify any questions where the content of the graph is not entirely intuitive.

Reviewer #3:

[…] I suspect that this study is not the end of the matter. In particular, it would be important to understand how local differences in cadherins affect junctional mechanics. The authors cite earlier work from the Mege lab indicating that cadherins can influence membrane mechanics. Whether this is at the level of the bilayer or via alterations in the cortical cytoskeleton would be important to address. But this is beyond the reasonable scope of a paper; indeed, it would speak to the potential for this study to motivate future research.

1. Figure 4G. Is this correct as currently presented? The authors describe this as showing that cadherin cluster size near non-shortening vertices is the same as that around the passive vertices in shortening junctions. But to my eye, what is drawn as the non-shortening data set looks similar to the set that is labelled as (active). Has something been mislabelled?

The data in Figure 4G are not incorrectly labeled. The difference between the active and non-shortening junctions is best observed by focusing on the upper end of the distribution where the active violin plot is noticeably wider than the non-shortening violin plot.

2. Embryo cohesion. This is measured as embryo survival at stage 23. But that seems to me to be a very indirect measure of tissue integrity. Changes in survival may reflect catastrophic loss of integrity, but miss more subtle features. I would be happy enough if they were to use the term "viability" instead of "cohesion". There is still a very interesting different in effect of the cis-mutant.

We appreciate this comment and have struggled with finding the correct term ourselves. Initially we used the term embryo survival instead of embryo cohesion but found this to but somewhat misleading. While the cis-mutant embryos do survive well past the chd3 knockdown embryos they do not survive to make adult animals. The updated manuscript now uses the term embryo integrity in place of embryo cohesion as integrity has less of a direct connection to adhesion than the term embryo cohesion.

3. I think that some of the analyses could be explained more intuitively for the general reader. For example, when the authors introduce their Straightness Index, it is not clear from the Results that they are talking about the straightness of motion of the vertices. (For junction folks, "straightness" sounds like the measures of junctional straightness that have been used as proxies of line tension.) It would only take a sentence to give an intuitive explanation in this and other instances.

As noted above we have updated the manuscript at a number of points to try and clarify the language for a general reader, including the section discussing the straightness index. For example:

Definition of Straightness Index. The following text was added to the main manuscript (pg.6) to clarify that Straightness Index referred to vertex motion and not bicellular junction “straightness”.

“Analysis of the straightness index, quantifying how straight vertices move along the in-line direction”.

The complete definition of Straightness index is given in the Appendix (section 12).

4. Glass-like behaviour in junctions. To what extent can one really say that the passive junctions are "more glass-like". If I read Figure 1E correctly, the exponent of "t" for the passive junctions is still >1 (1.3 from Figure 1E). So, is it more helpful to simply regard them as less fluidized, rather than invoking subdiffusive behaviour (which would require the exponent to be <1)? I'm happy to the corrected by the authors (or the other reviewers), but beyond a point of phenomenology I'm still not sure that I can see an underlying intuition that would be really helpful.

Along these lines, is it possible to statistically compare the differences in the exponentials?

5. "Non-shortening" junctions. Were these tested away from junctions that shortened? What about the junctions that also contribute to the vertices at the ends of the junctions that shortened? Did these show any asymmetry in mechanics or in cadherin clustering?

A good question. The non-shortening junctions were tested away from the junctions that shortened and we have not performed a complete analysis comparing “close” versus “far” non-shortening junctions. We will consider this in future work.

https://doi.org/10.7554/eLife.65390.sa2

Article and author information

Author details

  1. Robert J Huebner

    Department of Molecular Biosciences, University of Texas, Austin, United States
    Contribution
    Conceptualization, Data curation, Formal analysis, Validation, Investigation, Visualization, Writing - review and editing
    Contributed equally with
    Abdul Naseer Malmi-Kakkada
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-8778-9689
  2. Abdul Naseer Malmi-Kakkada

    1. Department of Chemistry, University of Texas, Austin, United States
    2. Department of Chemistry and Physics, Augusta University, Augusta, Georgia
    Contribution
    Conceptualization, Data curation, Software, Formal analysis, Visualization, Methodology, Writing - review and editing
    Contributed equally with
    Robert J Huebner
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-5429-4652
  3. Sena Sarıkaya

    Department of Molecular Biosciences, University of Texas, Austin, United States
    Contribution
    Investigation, Visualization
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-5008-2065
  4. Shinuo Weng

    Department of Molecular Biosciences, University of Texas, Austin, United States
    Contribution
    Investigation, Methodology
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-7932-913X
  5. D Thirumalai

    Department of Chemistry, University of Texas, Austin, United States
    Contribution
    Formal analysis, Supervision, Funding acquisition, Visualization, Project administration, Writing - review and editing
    For correspondence
    dave.thirumalai@gmail.com
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-1801-5924
  6. John B Wallingford

    Department of Molecular Biosciences, University of Texas, Austin, United States
    Contribution
    Conceptualization, Supervision, Funding acquisition, Writing - original draft, Project administration, Writing - review and editing
    For correspondence
    wallingford@austin.utexas.edu
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-6280-8625

Funding

Eunice Kennedy Shriver National Institute of Child Health and Human Development (R01HD099191)

  • John B Wallingford

National Science Foundation (Phys 17-08128)

  • D Thirumalai

Welch Foundation (F-0059)

  • D Thirumalai

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

We thank Dan Dickinson for use of the iSIM microscope and for critical reading and helpful discussions. We thank Andy Ewald for critical reading of the manuscript. This work was supported by grants from the NICHD (R21HD084072) and the NIGMS (R01GM104853) to JBW and from the NSF (Phys 17–08128) and the Collie-Welch Chair through the Welch Foundation (F-0059) to DT.

Ethics

Animal experimentation: Animal work described here was performed in accordance with the UT Austin Institutional Animal Care and Use Committee protocol #AUP-2018-00225.

Senior Editor

  1. Kathryn Song Eng Cheah, The University of Hong Kong, Hong Kong

Reviewing Editor

  1. Danelle Devenport, Princeton University, United States

Reviewer

  1. Alpha Yap, University of Queensland, Australia

Publication history

  1. Received: December 2, 2020
  2. Accepted: May 1, 2021
  3. Accepted Manuscript published: May 25, 2021 (version 1)
  4. Version of Record published: June 15, 2021 (version 2)

Copyright

© 2021, Huebner et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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