Discrete regions of the tailbud exhibit unique patterns of cell flow

Using 4D confocal imaging and cell tracking, we examined the cell flow of the paraxial mesoderm and its progenitors during trunk elongation (Fig. 1A). We divided the tracks into three tailbud regions based on morphology and patterns of gene expression. The dorsal medial zone (DM) lies in the posterior tailbud dorsal to the axial and paraxial mesoderm (Fig. 1C,D, red domain) and contains recently identified bipotential neural/mesodermal stem cells (Martin and Kimelman, 2012). The DM lacks expression of mesoderm and segmentation genes, such as tbx6 and her1 (Griffin et al., 1998; Holley et al., 2000). The progenitor zone (PZ) is ventral to the DM and posterior to the notochord (Fig. 1C,D, green domain) and exhibits tbx6 and her1 transcription. The presomitic mesoderm (PSM) consists of two bilateral columns of cells (Fig. 1C,D, cyan domains) that display the her1 stripes created by the segmentation clock (Holley et al., 2000; Pourquié, 2011). The PSM is covered with an extracellular matrix that separates it from the overlying DM and adjacent axial mesoderm (Jülich et al., 2009). Generally, the PSM exhibits much less cell movement than does the posterior tailbud (Mara et al., 2007).

• Download figure
• Open in new tab
• Download powerpoint

Fig. 1.

Cell movement in the wild-type zebrafish tailbud. (A) Confocal image stacks of RFP-labeled nuclei were taken through time and nuclei were tracked in 4D. (B) Independent tracking of red and green double-labeled nuclei revealed cell tracking to be 85% accurate. (C) Cell tracks were divided into regions of interest: dorsal medial zone (DM; red), progenitor zone, (PZ; green), presomitic mesoderm (PSM; cyan). (D) A lateral view of the image shown in C. (E) Examination of mean track speeds. P-values calculated using ANOVA with additional validation by permutation tests. The DM and PZ speeds are equivalent (DM vs PZ, P>0.05) and are higher than PSM (DM vs PSM, P<0.05; PZ vs PSM, P<0.05). (F) The means of the coefficient of variation (CV) of track speed show that the CV increases from the DM to PZ (P<0.05) and from the PZ to PSM (P<0.05). (G-I) Two-photon labeling of DM cells at the ten-somite stage. (G) Dorsal view. (H) Lateral view. (I) After completing elongation, the uncaged cells differentiated as myofibers. A-C and G are dorsal views. In all panels, anterior is left the right except panel I in which anterior is up.

We found the cell tracking to be 85% accurate over the 2.5-3 hour dataset (Fig. 1B; Materials and methods) and utilized the cell tracks to examine the general patterns of movement in the tailbud including track straightness, mean speed and coefficient of variation (CV; standard deviation divided by the mean) of the speed (Fig. 1E,F; supplementary material Fig. S1A-D; Fig. S2A-D). Independent fate mapping was used to define the longer-term flow of cells during trunk growth. We labeled clusters of approximately five cells in the DM by two-photon uncaging of caged fluorescein at the ten-somite stage (Fig. 1G,H) and allowed the embryos to complete body elongation (Fig. 1I). Of 13 embryos, ten exhibited labeled myofibers, indicating that DM cells migrated through the PZ to the PSM and were incorporated into somites. The separation of the myofibers by up to eight somites indicates that the labeled cells resided in the PZ for different lengths of time and entered the PSM up to 3-4 hours apart.

Utilizing the raw cell track data, we compared the statistics of cell motion in the DM, PZ and PSM. Cell movement within the DM was rapid, showed low CV and exhibited the straightest trajectories (Fig. 1E,F; supplementary material Fig. S1A-D, Fig. S2A-D). PZ cell movement was equally rapid, but displayed greater CV of track speed and reduced ‘straightness’ relative to the DM. The PSM mean speed was much diminished, had high CV of track speed and the tracks were the least straight.

These changes in cell motion are visualized with a vector map in which the 3D cell velocities are projected onto the two-dimensional (2D) x and y planes and averaged over 10 μm² sectors and in the z direction (Fig. 2A). Movement within each sector is averaged for the length of the movie with speed indicated by heat map and projected velocity by arrow orientation and length. The vector maps show the rapid cell movement in the posterior tailbud and the gradual decrease in motion in the PSM. The vectors reveal the posteriorly directed motion of the DM and swirls of cells moving from the medial to lateral PZ (Fig. 2A; supplementary material Fig. S3A-D). A similar swirling pattern is observed in the tailbud of avian embryos (Bénazéraf et al., 2010; Zamir et al., 2006). This flow pattern in the zebrafish PZ was also visualized by displaying the top 10% of tracks with the largest displacement in each direction (Fig. 2D,G; supplementary material Fig. S4A-D). Here, the ventral migration from the DM into the PZ was highlighted in the medial-posterior tailbud. This flow is segregated from the dorsal and anterior migration of the lateral periphery. We used finite element method (FEM) to quantify local rotational velocity within the flow field defined by the trajectories of the cell nuclei (Kelley and Ouellette, 2011). The rotation is displayed similarly to the velocity field, but the heat map indicates the magnitude of the local rotation and the arrows represent the projection of vorticity vectors. The direction of the arrows is perpendicular to the plane of rotation via the ‘right-hand rule’. A dorsal-to-ventral rotation exists within the DM and medial PZ (Fig. 2J; supplementary material Fig. S5A-D).

• Download figure
• Open in new tab
• Download powerpoint

Fig. 2.

Cell flow in the zebrafish tailbud. Wild-type (A,D,G,J), notum1a-overexpressing (B,E,H,K) and SU5402-treated (C,F,I,L) embryos. (A-C) The vector displacement map averages cell motion in discrete sectors. The heat map indicates mean speed with warmer colors indicating higher speeds and arrows signifying averaged 3D velocity vectors. See also supplementary material Fig. S3. (D-I) The top 10% of individual PZ tracks exhibiting the greatest displacement in each direction (green, dorsal to ventral; yellow, medial to lateral; red, posterior to anterior; blue, ventral to dorsal). See also supplementary material Fig. S4. (J-L) 3D finite element method was used to measure the local rotation in the flow of cells. Arrows slanting rightward indicate a dorsal-to-ventral local rotation whereas leftward-slanting arrows signify a ventral-to-dorsal local rotation.

A transition from effective and coherent cell flow as cells move from the DM to the PZ

To examine local tissue motion, we averaged cell velocities over different radii (5, 10, 15, 20, 25, 30, 35, 40 μm) and displayed the velocity in a vector map. The map averaged over the 15 μm radius is representative and is shown next to the cell velocity vector map of the raw data (Fig. 3A,B). We then subtracted the average tissue motion from the individual tracks to display cell velocity variation from the local tissue average (Fig. 3C). This analysis demonstrated that local tissue motion in the PSM is small compared with local tissue motion in the DM (Fig. 3B). Cellular variation from local tissue movement was also low in the PSM, particularly relative to the PZ (Fig. 3C). These general patterns are present when averaging velocities at all radii. However, averaging over larger radii leads to artifacts as local velocities in the DM appear reduced owing to averaging with adjacent slower PSM cells. Thus, to quantitatively examine cell motion, we analyzed the DM, PZ and PSM tracks separately.

• Download figure
• Open in new tab
• Download powerpoint

Fig. 3.

Quantitative metrics reveal changes in tissue fluidity. (A) A vector map of cell velocities. Warmer colors represent higher velocities and arrows indicate the 2D projection of the averaged 3D velocity vectors. (B) A vector map of local tissue velocity averaged over a 15 μm radius. (C) A vector map of cell velocity variation from local tissue velocity. (D-O) Data for four wild-type zebrafish embryos (D-G), three notum1a-overexpressing embryos with elongation defects (H-K) and three SU5402-treated embryos with elongation defects (L-O). (D) The MSD exponent indicates that the movement is a combination of ballistic and Brownian motion for all regions with the DM being the most directed (DM vs PZ, P<0.05; DM vs PSM, P<0.05). Motion in the DM is strongly polarized (DM vs PZ, P<0.05; DM vs PSM, P<0.05) (E), has the largest length scale over which direction of motion is correlated (DM vs PZ, P<0.05; DM vs PSM, P<0.05) (F) and exhibits highest neighbor similarity (G). (H) MSD is not significantly changed in notum1a-overexpressing embryos (DM, P>0.05). However, notum1a reduces the polarization (P<0.05) (I), correlation length (P<0.05) (J) and neighbor similarity (K) of the DM. (L) MSD in the DM is reduced in SU5402-treated embryos (P<0.05). In addition, SU5402 treatment reduces the polarization (P<0.05) (M), correlation length (P<0.05) (N) and neighbor similarity (O) of the DM. P-values calculated using Student's t-test.

Time lapses of the entire developing embryo show that cells in a given somite, e.g. somite ten, do not move relative to the body axis. Rather, the posterior tip of the tailbud progressively extends away from somite ten (Karlstrom and Kane, 1996; Schröter et al., 2008). Our analysis of local average velocity found that the PSM also displayed relatively little movement (Fig. 3A,B). The lack of net displacement along the anterior-posterior axis in the anterior part of the PSM was also evident. Thus, we used the anterior 50 μm of the PSM as our frame of reference. We calculated the center of mass of the velocities of the bilateral halves of the anterior 50 μm of the PSM in our datasets for each time point and subtracted the movement of this center of mass from all other individual cell velocities for each time point. We used these relative velocities to calculate the value of the mean square displacement (MSD) exponent, polarization (Φ), correlation length of direction of motion, neighbor similarity, polar angle (ϕ), and convergence and extension as described below.

We calculated the MSD for each track and extracted the corresponding exponent values. An exponent value of 1 indicates pure diffusive motion and a value of 2 indicates ballistic motion. The data from four wild-type embryos were averaged for the DM, PZ and PSM. Cells in all three domains exhibited values between 1 and 2, indicative of directed migration (Fig. 3D). The DM exhibited a larger exponent value, consistent with it displaying the straightest and most rapid cell migration.

Neighbor similarity is a measure of the degree to which a cell migrates in the same direction as its immediate neighbors (Arboleda-Estudillo et al., 2010). The DM cells showed higher neighbor similarity than those of the PZ or PSM (Fig. 3G). We also quantified the global order in each domain via the polarization (Φ) which varies from 0 (disordered) to 1 (ordered) (Cavagna et al., 2010). The DM exhibited high polarization that was roughly twice that observed in the PZ or PSM, indicating that cells migrate more coherently in the DM (Fig. 3E). This loss of coherence as cells migrate into the PZ is reflected in the increase in the variation of individual cell motion relative to the local tissue motion in the PZ (Fig. 3C).

Lastly, we calculated the two-point correlation function of the normalized velocities (Angelini et al., 2010; Cavagna et al., 2010). As expected from the general geometry of the cell flow, the correlation length of the direction of motion was relatively high in the DM (~15 cell diameters) but dropped significantly as cells entered the PZ and remained low in the PSM (Fig. 3F).

Together, these data indicate that cell flow in the DM is rapid, ordered and posteriorly directed. As the cells enter the PZ, their speed is maintained but motion becomes less straight and less effective as migration loses much of its coherence and local coordination. Speed decreases as cells transition from the PZ to the PSM, and motion coherence continues to be low.

Reduction in Wnt signaling abrogates coherence of DM cell migration and bilateral symmetry in the PZ

The cell flow field analysis indicates that DM cells migrate coherently to the posterior end of the embryo where they adopt a less coordinated mode of cell migration. We found that this transition coincides with the expression of a number of Wnt inhibitors, including notum1a (Fig. 4C) (Flowers et al., 2012; Giráldez et al., 2002; Traister et al., 2008). notum1a, like a recently characterized planarian notum homolog, specifically inhibits canonical Wnt signaling and can do so when overexpressed during body elongation (Flowers et al., 2012; Petersen and Reddien, 2011). Canonical Wnt signaling operates within a gene network required for zebrafish axis elongation, and we reasoned that notum1a might regulate cell migration in the tailbud (Shimizu et al., 2005; Szeto and Kimelman, 2004; Thorpe et al., 2005). We overexpressed notum1a by mRNA microinjection and observed axis elongation defects (Fig. 4D,E; supplementary material Fig. S6). We performed qPCR on pooled dissected tailbuds to assay for changes in canonical Wnt target gene and mesoderm specific transcription. Consistent with notum1a inhibiting Wnt signaling, we detected a strong reduction in expression of dkk1, a downstream target of canonical Wnt signaling, but not in expression of the Fgf targets sef (il17rd – Zebrafish Information Network) and sprouty4 (Fig. 4N) (Fürthauer et al., 2002; Fürthauer et al., 2001; Hashimoto et al., 2000; Shinya et al., 2000; Tsang et al., 2002). We also observed a significant reduction in tbx6 expression suggesting a reduction in mesodermal cell fate. However, in situ hybridization for mesodermal markers such as tbx6, her1 and eve1 or the neural marker neurogenin 1 suggests that the notum1a embryos with the misdirected body axes retain normally organized mesodermal and neural cell tissue (Fig. 4F,G,K,L; supplementary material Fig. S6) (Joly et al., 1993; Korzh et al., 1998).

• Download figure
• Open in new tab
• Download powerpoint

Fig. 4.

Ectopic notum1a expression or SU5402 treatments perturb axis elongation. (A-M) Wild-type (A-C,F,K), notum1a-overexpressing (D,E,G,L) and SU5402-treated (H-J,M) zebrafish embryos. (C) notum1a is transcribed in the posterior DM. (D) Ectopic notum1a gives rise to a shortened axis and malformed tailbud. (E) Half of these embryos develop severely misdirected body axes. Spatial expression of tbx6 (F-H) and neurogenin1 (K-M) remains relatively normal despite notum1a overexpression (G,L) or SU5402 treatment (H,M). (I,J) SU5402 treatment gives rise to a mild axis elongation defect. (N) qPCR of dissected tailbuds after notum1a overexpression reveals reductions in transcription of dkk1 and tbx6. Student's unpaired t-test. *P≤0.05. n=4. Error bars represent s.e.m.

Owing to difficulty imaging embryos with severely upturned body axes (supplementary material Fig. S6Q), we sorted eight-somite-stage notum1a-overexpressing embryos exhibiting mild elongation defects for time-lapse imaging (Fig. 4D). At the eight-somite stage, we have a 50% likelihood of identifying embryos that ultimately have elongation defects. Roughly half of the sorted embryos developed normal trunks and tails, whereas the other half exhibited misdirected trunks pointing dorsally, leftward or rightward (Fig. 4E; supplementary material Fig. S6). Accordingly, of the six notum1a-overexpressing embryos that we imaged, three had cell velocity fields similar to wild type whereas three were clearly abnormal. These latter three embryos displayed an obvious cell aggregation on the dorsal tailbud. The abnormal embryos exhibited no significant change in either track straightness or mean cell speeds (supplementary material Fig. S1E-G, Fig. S2E-G).

The effects of ectopic notum1a expression on cell motion can be seen in the asymmetries in vector maps (Fig. 2B; supplementary material Fig. S3E-G). The medial posterior tailbud still exhibited relatively rapid, posteriorly biased cell movement, but the bilateral swirls in the PZ were absent. Similarly, the top 10% track displacement shows that the ventral and dorso-anterior flows were no longer segregated and bilaterally symmetric (Fig. 2E,H; supplementary material Fig. S4E-G). The vorticity vector map reveals that the dorsal-ventral local rotation in the flow field was disrupted and, in some cases, even reversed exhibiting ventral to dorsal rotation (Fig. 2K; supplementary material Fig. S5E-G).

These notum1a-overexpressing embryos showed no significant alteration in the value of the MSD exponent (Fig. 3H). However, when we examined the effects of notum1a overexpression on cell motion in the DM, we observed reduced neighbor similarity (Fig. 3K), polarization (Φ) (Fig. 3I) and correlation length of the direction of motion (Fig. 3J). The PZ and PSM were not significantly affected (Fig. 3H-K).

We also used a heat-shock dominant-negative Tcf-GFP transgenic zebrafish line (hsΔTCF-GFP) to inhibit canonical Wnt signaling (Lewis et al., 2004). Heat shock of this line at the two-somite stage resulted in more severe abrogation of development than did injection of notum1a mRNA (Yin et al., 2011), and exhibited more severe quantitative effects on cell motion (supplementary material Fig. S7). Together, these data suggest that inhibition of canonical Wnt signaling in the tailbud reduces the coherence of migration in the DM.

Inhibition of Fgf signaling reduces DM cell migration coherence but not bilateral symmetry in the PZ

To examine Fgf signaling in the zebrafish tailbud, we performed a series of time-resolved perturbations with the Fgfr antagonist SU5402 and quantified the onset of inhibition. We measured phosphorylation levels of the effectors Erk and Akt by western blot, and transcription of the direct Fgf targets sprouty4 and sef by qPCR. We observed notable signal reduction in pooled dissected tailbuds after three hours treatment with SU5402 (Stulberg et al., 2012). This treatment led to a much milder effect on axis elongation than did notum1a inhibition of Wnt signaling (Fig. 4I,J). No bump formed in the DM and trunk elongation was linear. However, the embryos were shorter than normal and frequently displayed a kink in the posterior tail. Like notum1a-overexpressing embryos, these SU5402-treated embryos have relatively normal patterns of mesodermal and neural gene expression (Fig. 4H,M) (Stulberg et al., 2012).

To examine the role of Fgfr signaling in regulating cell flow within the tailbud, we began 4D confocal time-lapse analysis three hours after SU5402 treatment and imaged six embryos. As with half of the notum1a-overexpressing embryos, three of the SU5402-treated embryos were wild type in their quantitative cell flow metrics (not shown). However, the other three embryos exhibited changes in the DM that were equal to or stronger than the alterations seen in embryos with ectopic notum1a, and the alteration in cell flow is visually obvious. Cell track mean speed was unchanged in the DM (supplementary material Fig. S2), but the CV of track mean speed was modestly increased in both the DM and PZ (data not shown). Examination of polarization (Φ), correlation length of the direction of motion and neighbor similarity revealed reductions in the DM in line with those observed after notum1a overexpression (Fig. 3M-O). Thus, the coherence of migration was significantly reduced. Inhibition of Fgfr signaling also strongly decreased the value of the MSD exponent and track straightness in the DM (Fig. 3L; supplementary material Fig. S1H-J). By comparison, track straightness was only weakly affected and the value of the MSD exponent was not changed by notum1a overexpression, suggesting that SU5402 treatment has a more robust effect on DM cell flow. Unlike notum1a overexpression, the SU5402 treatment caused neither a loss of bilateral symmetry in the flow pattern of the posterior tailbud (Fig. 2C,F,I; supplementary material Fig. S3H-J, Fig. S4H-J) nor a reversal in local rotational velocity (Fig. 2L; supplementary material Fig. S5H-J). Thus, whereas Fgfr inhibition more strongly affected quantitative metrics of cell flow in the DM, ectopic notum1a-overexpressing embryos displayed more dramatic alterations in dorsal-to-ventral rotation and bilateral symmetry of flow in the PZ and in overall axis morphology.

Tissue fluidity is regulated by Cadherin 2

cadherin 2 (cdh2) is required for normal tailbud morphology and axis elongation but not tailbud differentiation (Hammerschmidt et al., 1996; Harrington et al., 2007; Lele et al., 2002; Warga and Kane, 2007) (Fig. 5A,B). We examined cell flow in cdh2-null mutants to determine whether tissue fluidity was affected in ways that paralleled abrogation of Wnt or Fgf signaling. The cdh2 mutant exhibited many of the same changes in cell motion but, overall, the effects on the quantitative metrics were stronger than those observed after either notum1a overexpression or SU5402 treatment (Fig. 5C-J). Loss of cdh2 reduced the MSD exponent in the DM (Fig. 5G). The cdh2 mutants also displayed reduction of the correlation length of the direction of motion both in the DM and PZ (Fig. 5I) and reduction of polarization (Φ) in all domains (Fig. 5H). We wondered whether abrogation of either Wnt or Fgf signaling could be affecting cell flow via partial diminution of Cadherin-dependent cell adhesion. Thus, we examined adherens junctions by immunohistochemistry for β-catenin. In wild-type tailbuds, visualization of β-catenin revealed a lattice of adherens junctions (Fig. 5K), and this lattice was blotchy in cdh2 mutants (Fig. 5L). However, we observed no obvious loss of adherens junctions in either notum1a-overexpressing or SU5402-treated tailbuds (Fig. 5M,N). These data suggest that reduction of Wnt or Fgf signaling in the tailbud does not primarily affect tissue fluidity by reducing Cadherin-dependent cell adhesion.

• Download figure
• Open in new tab
• Download powerpoint

Fig. 5.

Loss of cadherin 2 reduces the effectiveness and coherence of cell motion in the zebrafish tailbud. (A,B) cdh2 mutants have morphologically abnormal tailbuds (A) and tails (B). (C-J) Quantitative analysis of cell motion in the tailbud of three wild-type embryos (C-F) and three cdh2 mutants (G-J). (G) MSD is reduced in the DM of cdh2 mutants (P<0.05). (H) Polarization is reduced in the DM (P<0.05), PZ (P<0.05) and PSM (P<0.05) of cdh2 mutants. (I) Correlation length is lower in the DM (P<0.05). (J) Neighbor similarity is diminished in the DM of cdh2 homozygotes. (K-N) Adherens junctions in the PZ are visualized by immunohistochemistry for β-catenin. All panels are at the same magnification; scale bar: 5 μm. The lattice of adherens junctions among cells is present in wild-type embryos (K) but is disrupted in cdh2 mutants (L). The pattern of adherens junctions in notum1a-overexpressing embryos (M) and SU5402-treated embryos (N) resembles the wild-type pattern. P-values calculated via Student's t-test.

The balance between the coherence and rate of cell flow determines axis morphology

Inhibition of both Wnt and Fgf signaling reduced the coherence of cell flow in the DM, but ultimately had different effects on trunk elongation. To explore further the dynamics of cell flow in the tailbud, we studied a 2D model of self-propelled motion similar to a model used previously to study the emergence of order in cellular migration (Szabó et al., 2006). For simplicity, the tailbud is modeled as a ‘T’ geometry in 2D with reflective boundaries (Fig. 6; supplementary material Fig. S8 and Appendix S1). The bottom of the ‘T’ is anterior and the top is posterior. The upper portion of the vertical column represents the DM whereas the intersection with the vertical and horizontal sections is the PZ. Cells are introduced at the bottom of the ‘T’ at a constant rate and flow upward through the left and right ends of the top of the ‘T’. In the model, two forces determine the motion of a cell at each time point: a self-propulsion of constant magnitude and the force resulting from interactions with the neighbors or the walls of the ‘T’ (supplementary material Fig. S8 and Appendix S1). The direction of the self-propulsion changes over time: it tends to align itself along the direction of motion but also experiences random fluctuations. To mimic the measured change in the coordination of cell motion at the DM-to-PZ transition, the noise in the angular alignment was set to be higher at the top of the ‘T’. This simulation produces a steady bilaterally symmetric flow, as observed in wild-type embryos (Fig. 6A). When instead noise in the angular alignment of the individual cells is increased throughout the vertical portion of the ‘T’, the flow becomes jammed (Fig. 6B). In the real embryo, we would expect such a jam to lead to expansion in the vertical direction (formation of a bump) or deviation of the tail axis. In the 2D simulation, jamming causes an accumulation of cells in the DM (Fig. 6B). However, unlike the posterior jam that forms after ectopic notum1a expression, the jams in the simulation form anywhere along the vertical portion of the ‘T’. Further simulations indicated that localization of cell aggregation to the top of the ‘T’ requires the noise in the angular alignment of the individual cells to be lower at the bottom of the ‘T’ than at the top. The prediction is that cells anterior to the DM, in what we call the anterior dorsal medial zone (ADM), should be more ordered than in the DM in notum1a-overexpressing tailbuds.

• Download figure
• Open in new tab
• Download powerpoint

Fig. 6.

Simulation of cell flow during trunk elongation. (A-C) Sample snapshots of cell positions obtained using computer simulations of a 2D model system of self-propelled particles with soft interactions. The upper portion of the vertical column of the ‘T’ represents the DM whereas the intersection between the vertical and horizontal sections is representative of the PZ. Arrows denote the instantaneous velocity of each cell. Cell density is displayed as a heat map with warmer colors indicating higher density. See also supplementary material Fig. S8. (A) Wild-type simulation. (B) In ectopic notum1a embryos, cells are introduced at the lower column at the same rate as in wild type, but ectopic notum1a causes cells to move with higher angular noise (now the same as that of the PZ). (C) To model inhibition of Fgfr signaling by SU5402 treatment, the rate of addition of cells to the lower column is reduced to half the rate in A and B. Cells move with same randomness as in the ectopic notum1a embryos, but the attenuated cell flow into the DM reduces the number of cells in the DM. The polarization (Φ), standard deviation (std) of angles of posterior migration and cell number of the DM (vertical column) are the averages from 100 simulations for each of the three conditions.

We compared the polarization (Φ) in the ADM and DM of three wild-type embryos, three notum1a-overexpressing embryos and three SU5402-treated embryos (Fig. 7A-C). In wild type, the polarization in both the ADM and DM was high (Fig. 7A). In embryos ectopically expressing notum1a, the ADM is always more ordered than the DM (Fig. 7B), which is consistent with the cell aggregation forming in the DM instead of the ADM as suggested by the simulations.

• Download figure
• Open in new tab
• Download powerpoint

Fig. 7.

Axis extension requires balance of cell flow rate and flow coherence. Wild-type (A,D,G,J,M), notum1a-overexpressing (B,E,H,K,N) and SU5402-treated (C,F,I,L,O) zebrafish embryos. In A-I, values for ADM and DM are connected by a line, in order to compare the two domains in the same embryo. Thus, each line represents a single embryo. (A-C) Polarization (Φ). (D-F) Wild-type ADM and DM (D) show low variance in the angle of posterior migration (ϕ). The variance is not significantly changed in notum1a-overexpressing embryos (E) but the ADM variance is increased in SU5402-treated embryos (F) relative to wild type (P<0.05), indicating progressively larger deviation from direct posterior migration. (G-I) The MSD is similarly high in the wild-type DM and ADM (G). notum1a-overexpressing DMs and ADMs have relatively high MSD, statistically indistinguishable from wild type, indicating continued effective migration (H). MSD is reduced in SU5402-treated embryos in the ADM compared with wild type (P<0.05) (I). (J) The wild-type rate of ADM convergence and extension. (K,L) notum1a-overexpressing ADMs (K) display wild-type levels of convergence and extension, but SU5402-treated ADMs (L) show reduced extension (P<0.05). P-values calculated using Student's t-test. (M) In wild type, a strong flow in the ADM and collective migration in the DM places cells at the posterior tip of the embryo. In the PZ, the coherence of the flow diminishes, which facilitates cell mixing and bilateral distribution of cells in the PZ. (N) In notum1a-overexpressing embryos, the coherence in the DM is prematurely lost but the flow rate in the ADM is maintained. Cells are unable to move through the tailbud and a ‘traffic jam’ forms leading to a bump and a turning of the axis. (O) In SU5402-treated embryos, the coherence in the DM is strongly reduced, as is the flux in the ADM. The latter reduction curtails the propensity of the flow to jam, thus cells pass through the PZ, albeit at a reduced rate, leading to a straight but shorter axis than that of wild type.

In the SU5402-treated embryos, the MSD exponent in the DM was decreased relative to wild type (Fig. 3D,L). This decline in effective migration in SU5402-treated embryos suggests an explanation for the different morphological phenotypes of notum1a and SU5402-treated embryos. In simulations, an increase in the disorder can be counterbalanced by a reduction in the flux of cells into the DM (Fig. 6C). This latter reduction curtails formation of jams in the flow (Fig. 6C) and bilateral flow is maintained. We examined posterior flow by calculating the medial-lateral angle of cell movement relative to direct posterior migration for each cell at each time point. The variability of posterior migration was calculated as the standard deviation of the polar angle (ϕ) distributions for the ADM and DM (Fig. 7D-F). In wild-type embryos, the angles tightly clustered near direct posterior migration. The distribution was broadest in SU5402-treated embryos. Thus, cells in the ADM and DM of SU5402-treated embryos were less posteriorly directed. The same trend is observed in the computer simulations (Fig. 6). The reduction in posteriorly directed migration was also evident in the effective migration of cells in the ADM and DM of SU5402-treated embryos. The MSD exponent of both domains was lower in SU5402-treated embryos, but not in notum1a-overexpressing embryos, relative to wild type (Fig. 7G-I). Lastly, we examined convergence towards the dorsal midline and extension along the anterior-posterior axis of the ADM and DM. We found that the ADM of SU5402-treated embryos displayed less extension than either wild-type or notum1a-overexpressing embryos (Fig. 7J-L). Thus, the flow of cells into the DM is lower after SU5402 treatment. These data, along with the simulations, suggest that the balance between the rate of cell flow and the coherence of the flow underpins the different elongation phenotypes in wild-type embryos, notum1a-overexpressing embryos and SU5402-treated embryos.