The vertex model accounts qualitatively and quantitatively for the observed packing geometry in the wing disc and its response to perturbation by laser ablation. Epithelial packing geometry is a consequence of both physical cellular properties and the disordering influence of proliferation. The occurrence of T2 transitions during network growth suggests that elimination of cells from the proliferating disc epithelium may be the result of junctional force balances.

Planar cell polarity (PCP) proteins form polarized cortical domains that govern polarity of external structures such as hairs and cilia in both vertebrate and invertebrate epithelia. The mechanisms that globally orient planar polarity are not understood, and are investigated here in the Drosophila wing using a combination of experiment and theory. Planar polarity arises during growth and PCP domains are initially oriented toward the well-characterized organizer regions that control growth and patterning. At pupal stages, the wing hinge contracts, subjecting wing-blade epithelial cells to anisotropic tension in the proximal-distal axis. This results in precise patterns of oriented cell elongation, cell rearrangement and cell division that elongate the blade proximo-distally and realign planar polarity with the proximal-distal axis. Mutation of the atypical Cadherin Dachsous perturbs the global polarity pattern by altering epithelial dynamics. This mechanism utilizes the cellular movements that sculpt tissues to align planar polarity with tissue shape.

Subdividing proliferating tissues into compartments is an evolutionarily conserved strategy of animal development [1-6]. Signals across boundaries between compartments can result in local expression of secreted proteins organizing growth and patterning of tissues [1-6]. Sharp and straight interfaces between compartments are crucial for stabilizing the position of such organizers and therefore for precise implementation of body plans. Maintaining boundaries in proliferating tissues requires mechanisms to counteract cell rearrangements caused by cell division; however, the nature of such mechanisms remains unclear. Here we quantitatively analyzed cell morphology and the response to the laser ablation of cell bonds in the vicinity of the anteroposterior compartment boundary in developing Drosophila wings. We found that mechanical tension is approximately 2.5-fold increased on cell bonds along this compartment boundary as compared to the remaining tissue. Cell bond tension is decreased in the presence of Y-27632 [7], an inhibitor of Rho-kinase whose main effector is Myosin II [8]. Simulations using a vertex model [9] demonstrate that a 2.5-fold increase in local cell bond tension suffices to guide the rearrangement of cells after cell division to maintain compartment boundaries. Our results provide a physical mechanism in which the local increase in Myosin II-dependent cell bond tension directs cell sorting at compartment boundaries.

Epithelia are sheets of cells that are dynamically remodelled by cell division and cell death during development. Here we describe the cell shapes and packings as networks of polygons: stable and stationary network configurations obey force balance and are represented as local minima of a potential function. We characterize the physical properties of this vertex model, including the set of ground states, and the energetics of topological rearrangements. We furthermore discuss a quasistatic description of cell division that allows us to study the mechanics and dynamics of tissue remodelling during growth. The biophysics of cells and their rearrangements can account for the morphology of cell packings observed in experiments.

Our results argue that natural selection acts predominantly on cell size and indirectly influences the spindle through the scaling of the spindle with cell size. Previous studies have shown that the spindle also scales with cell size during early development. Thus, the scaling of the spindle with cell size controls its variation over both ontogeny and phylogeny.

Spindle microtubules, whose dynamics vary over time and at different locations, cooperatively drive chromosome segregation. Measurements of microtubule dynamics and spindle ultrastructure can provide insight into the behaviors of microtubules, helping elucidate the mechanism of chromosome segregation. Much work has focused on the dynamics and organization of kinetochore microtubules, that is, on the region between chromosomes and poles. In comparison, microtubules in the central-spindle region, between segregating chromosomes, have been less thoroughly characterized. Here, we report measurements of the movement of central-spindle microtubules during chromosome segregation in human mitotic spindles and Caenorhabditis elegans mitotic and female meiotic spindles. We found that these central-spindle microtubules slide apart at the same speed as chromosomes, even as chromosomes move toward spindle poles. In these systems, damaging central-spindle microtubules by laser ablation caused an immediate and complete cessation of chromosome motion, suggesting a strong coupling between central-spindle microtubules and chromosomes. Electron tomographic reconstruction revealed that the analyzed anaphase spindles all contain microtubules with both ends between segregating chromosomes. Our results provide new dynamical, functional, and ultrastructural characterizations of central-spindle microtubules during chromosome segregation in diverse spindles and suggest that central-spindle microtubules and chromosomes are strongly coupled in anaphase.

The spindle shows remarkable diversity, and changes in an integrated fashion, as cells vary over evolution. Here, we provide a mechanistic explanation for variations in the first mitotic spindle in nematodes. We used a combination of quantitative genetics and biophysics to rule out broad classes of models of the regulation of spindle length and dynamics, and to establish the importance of a balance of cortical pulling forces acting in different directions. These experiments led us to construct a model of cortical pulling forces in which the stoichiometric interactions of microtubules and force generators (each force generator can bind only one microtubule), is key to explaining the dynamics of spindle positioning and elongation, and spindle final length and scaling with cell size. This model accounts for variations in all the spindle traits we studied here, both within species and across nematode species spanning over 100 million years of evolution.

Transient nuclear envelope (NE) ruptures in the Caenorhabditis elegans zygote are caused by a weakened nuclear lamina during nuclear positioning. Dynein-pulling forces enhance the severity of ruptures, while lamin restricts nucleocytoplasmic mixing and allows stable NE repair. This work is the first mechanistic analysis of NE rupture and repair in an organism.