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 extendingDrosophilagermband 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 theDrosophilagermband predict the onset of rapid cell rearrangement in both wild-type andsnail twistmutant 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.

Mitochondria are dynamic organelles found in almost all eukaryotic cells and perform several key cellular functions such as generating energy, triggering cell differentiation, and initiating cell death. They have their own DNA (mtDNA) and often come in multiple genetic varieties within a single cell. Dynamical processes such as mitochondrial fission, fusion, autophagy, and mitotic segregation can enable a mitochondrion population to eventually dominate the mitochondria genomic pool, sometimes with devastating consequences. Therefore, understanding how changes in mtDNA accumulate over time and are correlated to changes in mitochondrial function can have a profound impact on our understanding of fundamental cell biophysics and the origins of some human diseases. Motivated by this, we develop and study a mathematical model to determine which cellular parameters have the largest impact on mtDNA population dynamics. The model consists of coupled differential equations to describe populations of healthy and dysfunctional mitochondria subject to mitochondrial fission, fusion, autophagy, and varying levels of cellular ATP. We study the time evolution of each population under specific selection biases and obtain a heat map in the parameter space of the ratio of the rates of fusion and autophagy of the healthy and dysfunctional populations. Our results may provide insights into how different mitochondrial populations survive and evolve under different selection pressures and with time.

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 Drosophila germband epithelium, which displays planar polarized myosin II and experiences anisotropic forces from neighboring tissues, and 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 Drosophila germband indicate a solid-to-fluid transition that corresponds to the onset of cell rearrangement and convergent extension in wild-type embryos and are also consistent with more solid-like behavior in bnt mutant embryos. Thus, the onset of cell rearrangement in the germband can be predicted by a combination of cell shape and alignment. 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.

Tunable mechanics and fracture resistance are hallmarks of biological tissues whose properties arise from extracellular matrices comprised of double networks. To elucidate the origin of these desired properties, we study...