Anisotropy links cell shapes to tissue flow during convergent extension

Abstract

<jats:p>Within developing embryos, tissues flow and reorganize dramatically on timescales as short as minutes. This includes epithelial tissues, which often narrow and elongate in convergent extension movements due to anisotropies in external forces or in internal cell-generated forces. However, the mechanisms that allow or prevent tissue reorganization, especially in the presence of strongly anisotropic forces, remain unclear. We study this question in the converging and extending<jats:italic>Drosophila</jats:italic>germband epithelium, which displays planar-polarized myosin II and experiences anisotropic forces from neighboring tissues. We show that, in contrast to isotropic tissues, cell shape alone is not sufficient to predict the onset of rapid cell rearrangement. From theoretical considerations and vertex model simulations, we predict that in anisotropic tissues, two experimentally accessible metrics of cell patterns—the cell shape index and a cell alignment index—are required to determine whether an anisotropic tissue is in a solid-like or fluid-like state. We show that changes in cell shape and alignment over time in the<jats:italic>Drosophila</jats:italic>germband predict the onset of rapid cell rearrangement in both wild-type and<jats:italic>snail twist</jats:italic>mutant embryos, where our theoretical prediction is further improved when we also account for cell packing disorder. These findings suggest that convergent extension is associated with a transition to more fluid-like tissue behavior, which may help accommodate tissue-shape changes during rapid developmental events.</jats:p>

Regionalized tissue fluidization is required for epithelial gap closure during insect gastrulation

“…While the recoil pattern after laser ablation supports the hypothesis of ventral tissue fluidization suggested by the shape index analysis, it has been recently shown that the relationship between shape index and tissue fluidity is non-linear when the tissue is under tension 26 . Since we obtained from laser ablations evidence that the Tribolium serosa exhibits a spatially inhomogeneous tension profile, we applied this extended theoretical framework.…”

“…Based on the vertex model, the leading theoretical framework for studying the mechanical behavior of epithelial tissues 25 , the theory predicts a critical value of shape index p = 3.81 marking the transition from a solid-like ( p < 3.81) to a fluid-like behavior ( p > 3.81 but see also ref. 26 and below). Our results showed that at Stage 3 ventral cells had on average a high shape index p of 4.25 characteristic of fluid-like tissues, unlike dorsal cells that had a significantly lower p value of 3.93.…”

“…The measurements were distortion-corrected using the above-mentioned Fiji plugins and plotted onto the segmented cartographic projection as a color map. The local cell shape alignment index Q was calculated as described recently 26 . Briefly, cells in each map projection were converted into a triangular mesh connecting the centers of all adjacent segmented cells, i.e., where three (or more) cells touch, a triangle (or a triangle fan) with vertices coinciding with centers of adjacent cells was formed.…”

“…For every cell, its shape alignment index Q became a weighted average over q from all triangles whose vertex coincides with this cell’s center. Using this Q , an adjusted shape index threshold was determined as p adj = p 0 + 4 bQ 2 for p 0 = 3.94 and b = 0.43 26 . According to Wang et al 26 , simulations of this threshold marks solid-to-fluid transition for a given anisotropy in the tissue (i.e., for a given value of cell shape alignment index Q ).…”

“…Using this Q , an adjusted shape index threshold was determined as p adj = p 0 + 4 bQ 2 for p 0 = 3.94 and b = 0.43 26 . According to Wang et al 26 , simulations of this threshold marks solid-to-fluid transition for a given anisotropy in the tissue (i.e., for a given value of cell shape alignment index Q ). The tissue fluidity for a given cell was then calculated as a difference between its actual shape index p and p adj for a given local value of Q .…”