Foams out of stable equilibrium: cell elongation and side swapping
The evolution of a liquid foam usually mixes quasi-equilibrium topological and geometrical features in an intricate way. We take advantage of special properties of ferro ̄uid froths and of constrained area evolution simulations, to distinguish the eects of side swapping (T1 processes) from other rearrangements in the froth. Cell elongation characterizes the froth and its deviation from mechanical equilibrium as robustly as the usually measured total wall length, that is surface energy. §
Hexagonal packing of Drosophila wing epithelial cells by the planar cell polarity pathway.
The mechanisms that order cellular packing geometry are critical for the functioning of many tissues, but they are poorly understood. Here, we investigate this problem in the developing wing of Drosophila. The surface of the wing is decorated by hexagonally packed hairs that are uniformly oriented by the planar cell polarity pathway. They are constructed by a hexagonal array of wing epithelial cells. Wing epithelial cells are irregularly arranged throughout most of development, but they become hexagonally packed shortly before hair formation. During the process, individual cell boundaries grow and shrink, resulting in local neighbor exchanges, and Cadherin is actively endocytosed and recycled through Rab11 endosomes. Hexagonal packing depends on the activity of the planar cell polarity proteins. We propose that these proteins polarize trafficking of Cadherin-containing exocyst vesicles during junction remodeling. This may be a common mechanism for the action of planar cell polarity proteins in diverse systems.
An introduction to human geography : the cultural landscape
1. Thinking Geographically 2. Population 3. Migration 4. Folk and Popular Culture 5. Language 6. Religion 7. Ethnicity 8. Political Geography 9. Development 10. Agriculture 11. Industry 12. Services 13. Urban Patterns 14. Resource Issues Conclusion