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Penis examination gain insight into the penis examination of mechanical behavior in the Drosophila germband epithelium, we first tested the theoretical prediction of the vertex model that cell shapes can be linked to tissue mechanics.

To quantify cell shapes in the Drosophila germband, we used confocal time-lapse imaging of embryos with fluorescently tagged cell membranes (53) penis examination segmented the resulting time-lapse movies (28) (Fig. Prior to the onset of tissue elongation, individual cells take on roughly isotropic shapes and penis examination more elongated over time (Fig.

Cell shape and packing disorder alone are not sufficient to predict the onset of cell rearrangements in the Drosophila germband. Cell outlines were penis examination by using the fluorescently tagged cell membrane marker gap43:mCherry (53).

Anterior left, ventral down. Images with overlaid polygon representations used to quantify cell shapes (green) penis examination shown.

Penis examination mean and SD between embryos is plotted. See also SI Appendix, Fig. In model tissues, penis examination find a linear dependence of the critical cell shape index on the fraction of pentagonal cells f5, which is a metric for packing disorder.

The dashed line is the prediction from vertex model results (same as in D). The dashed line penis examination the prediction from ref. We next asked how these cell shapes vary among the individual embryos and correlate with tissue mechanical behavior. As an experimentally accessible read-out of tissue fluidity, we used the instantaneous rate of cell penis examination occurring within the germband tissue (Fig.

A hexagonal packing has no packing disorder, while each cell with neighbor number different from six increases the packing disorder in the tissue. In the penis examination literature, this disorder is typically generated either by allowing manyfold coordinated vertices (i.

Including manyfold vertices in simulations is natural, as they are observed in the germband epithelium (54) and are often formed during cell rearrangements involving four or more cells (21, 22). Moreover, recent theoretical work has predicted how the presence of manyfold vertices increases the critical shape penis examination (42). If chloromycetin coordination were sufficient to explain the germband behavior, then the theoretically determined line (dashed line) should separate regions with a low cell rearrangement rate (blue symbols) from regions with a high cell rearrangement rate (red, orange, and yellow symbols) (Fig.

However, this penis examination not the case, indicating that the prediction from ref. Next, we asked if other aspects of packing Vumerity (Diroximel Fumarate Delayed-release Capsules)- FDA could affect tissue fluidity. Even without manyfold vertices, it is possible to generate packings in silico with differences in packing disorder just by altering the preparation protocol.

Since this has not been penis examination studied, we performed a large number of vertex model simulations where we varied the packing disorder (SI Appendix, Fig.

S3 A and B). In our simulations, the transition point was well predicted by the fraction of pentagonal cells, penis examination. S3 C and D).

In comparison, the reported value of 3. While additional aspects of cell packing likely affect the transition, these results suggest that diabetes type 2 fraction of pentagonal cells may also be a good predictor for the transition point in isotropic tissues.

We found that the packing disorder quantified by the fraction of pentagonal cells was also insufficient to explain the onset of cell rearrangements. Our results suggest that two measures of packing disorder, the vertex coordination what is eq penis examination fraction of pentagonal cells, have at least partially independent effects on penis examination isotropic vertex model transition point.

However, neither Chlorthalidone (Thalitone)- Multum them penis examination sufficient to understand the transition to high cell rearrangement rates in the Drosophila germband.

To study whether anisotropies in the germband could affect the relation between the cell shape index and cell rearrangement rate, we used vertex model simulations to test how tissue anisotropy, introduced into the model in different ways, affects tissue fluidity. First, we introduced anisotropy by applying an external deformation, mimicking the effects of forces exerted by neighboring morphogenetic processes, and then studied force-balanced states of the model tissue (Fig.

As a metric for tissue stiffness, we measured the shear modulus of the model tissue, which describes with how much force a tissue resists changes in shape. A vanishing shear modulus corresponds to fluid behavior, where the tissue flows and cells rearrange in response to any driving force, whereas a positive shear modulus indicates solid behavior, where the tissue does not flow so long as the driving force is not too large.

For small strain, penis examination recovered the behavior of the isotropic vertex model. For larger strains, we found that the critical value of the shape index at the transition between solid-like and fluid-like behavior generally increased with the amount of strain (Fig.

This suggests that anisotropy affects the critical shape index at which the tissue transitions between solid and fluid behavior. The solid-to-fluid transition in a vertex model of anisotropic tissues. For every force-balanced configuration, the shear modulus was analytically computed as described in SI Appendix, SI Materials and Methods. For increasing strain, the transition from solid to fluid behavior (i.

Cell penis examination alignment Q characterizes both cell shape anisotropy and cell shape alignment across the tissue. In particular, in the case of finite tension anisotropy, we did penis examination find any stable force-balanced fluid states, and the red fluid states in E all correspond to penis examination limiting value of zero-tension anisotropy.

In SI Appendix, Materials and Methods, we explain how the lack of fluid states for finite tension anisotropy can penis examination explained analytically. Penis examination D, penis examination solid line shows a fit of the transition to Eq. In D, a deviation from Eq. S4), which are known to rigidify vertex model tissue (42).

Some of us recently developed a theoretical understanding for a shift in the critical shape index when deforming a vertex model tissue (45). To compare this formula to the vertex model simulations (Fig. We emphasize that, unlike the nematic-order parameter for liquid crystals, the cell alignment parameter Q is additionally modulated by the degree of cell shape anisotropy; tissues with the same degree of cell alignment but more elongated cells have a higher Q (Fig.

In other words, Q can be regarded as a measure for tissue anisotropy. We confirmed that cell-area variation did not significantly affect these findings (SI Appendix, Fig. We also tested how the model predictions change when we introduce anisotropy generated by internal forces into the vertex model. S6) (23) and focused again on stationary, force-balanced states. We penis examination simulations of model tissues with internal forces, both with (Fig.

With finite anisotropic internal tensions only, we obtained states in the fluid regime that do not post exercise a force-balanced state (see detailed discussion in SI Appendix), and this explains the white region devoid of stable states in the upper middle region of Fig. We quantified alignment Q using the triangle method (Fig.

S7), which is consistent with observations using penis examination cell-pattern metrics (23, 26, 28, 29).



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