Simple forces, complex shapes

Abstract

Form follows physics in the fly eye, say Sascha Hilgenfeldt, Sinem Erisken, and Richard Carthew (Northwestern University, Evanston, IL). Figure 1 Shapes predicted by energy minimization modeling (red lines) match the outlines of cells in the fly eye. The idea that a small set of physical forces governs the shape of tissues goes back at least a hundred years, but there has been little evidence to support it. Now, Hilgenfeldt et al. show that just two parameters—cell elasticity and adhesion strength—can account for the arrangement of cells in the ommatidium, the 20-cell subunit of the fly's compound eye. The geometry of the cone cells in the center of the ommatidium resembles groups of soap bubbles, says Hilgenfeldt, who studies the physics of bubbles, foams, and other “soft solids.” This arrangement suggested that, as in bubble aggregates, adhesion and elasticity might help determine shape. And like bubbles, the cells might be minimizing the surface energy at their interface. To test this theory, the authors created a computer-simulated model of ommatidium geometry. Adhesion in these structures is supplied by cadherins at the cells' apicolateral surfaces. The elasticity of the cell membrane arises from a number of complex interactions between the lipid bilayer and the cytoskeleton but can be characterized by its resistance to deformation. The team found that beginning with cells of random shapes, and then adjusting the relative strengths of cadherin binding and membrane elasticity to minimize the total surface energy of all the cells, they could precisely reproduce the observed geometries of the eye. The model also predicted the abnormal cellular arrangements that are found in various cadherin mutants. “Even a small variation in adhesion can alter cell packing dramatically,” Carthew says. Can other tissue geometries be explained as simply? “We think these results stand as an example for less-ordered epithelia,” Carthew says, though some element of random variation may be needed in the mix to account for these structures. They also hope to model developmental changes with the same principles. “You could imagine that tissues undergoing morphogenesis go through a series of minimal energetic states, dictated by changes in a few factors that regulate cell interactions,” Carthew says, such as placement and number of adhesion molecules or cytoskeletal alterations. Reference: Hilgenfeldt, S., et al. 2008. Proc. Natl. Acad. Sci. USA. 10.1073/pnas.0711077105 [PubMed] [Cross Ref]