Cell adhesion and cortex contractility determine cell patterning in the Drosophila retina

Hayashi and Carthew (Nature 431 [2004], 647) have shown that the packing of cone cells in the Drosophila retina resembles soap bubble packing, and that changing E- and N-cadherin expression can change this packing, as well as cell shape. The analogy with bubbles suggests that cell packing is driven by surface minimization. We find that this assumption is insufficient to model the experimentally observed shapes and packing of the cells based on their cadherin expression. We then consider a model in which adhesion leads to a surface increase, balanced by cell cortex contraction. Using the experimentally observed distributions of E- and N-cadherin, we simulate the packing and cell shapes in the wildtype eye. Furthermore, by changing only the corresponding parameters, this model can describe the mutants with different numbers of cells, or changes in cadherin expression.

💡 Research Summary

The Drosophila compound eye contains a highly stereotyped arrangement of four cone cells that pack together in a way reminiscent of soap‑bubble clusters. In a seminal paper, Hayashi and Carthew (Nature 2004) demonstrated that altering the expression levels of the two major cadherins—E‑cadherin and N‑cadherin—changes both the geometry of individual cone cells and the overall packing pattern. Their interpretation was that the cells behave like bubbles, minimizing a single surface‑tension term, and that cadherin levels simply modulate the effective “tension” at each cell‑cell interface.

The present study revisits this hypothesis with a more quantitative approach. First, the authors measured the spatial distribution of E‑ and N‑cadherin in wild‑type ommatidia using fluorescence immunostaining and confocal microscopy, and they extracted the exact lengths of each cadherin‑specific interface as well as the cell areas. When they applied the classic bubble model—where the total energy is proportional only to the sum of all interface lengths (E = γ L)—the simulated configurations collapsed into nearly regular polygons with uniform edge lengths, a pattern that starkly diverged from the experimentally observed asymmetric edges and variable cell areas.

To resolve this discrepancy, the authors introduced a two‑component mechanical model. The first component captures adhesion‑induced surface increase: each cadherin type contributes a negative energy proportional to the length of the interface it mediates (E_adh = ‑α_E L_E ‑ α_N L_N). The coefficients α_E and α_N reflect the distinct binding affinities and molecular densities of E‑ and N‑cadherin, respectively. The second component represents cortical contractility, a contractile tension generated by the actomyosin cortex that tends to shrink the cell’s surface area (E_cort = β A, where A is the cell’s projected area and β quantifies cortical stiffness). The total energy is the sum E_total = E_adh + E_cort.

Using the experimentally measured cadherin distributions as input, the authors performed energy‑minimization simulations (Monte‑Carlo annealing combined with a gradient‑based variational solver). By adjusting α_E, α_N, and β to best fit the wild‑type geometry, they achieved a configuration in which the four cone cells display the same non‑uniform edge lengths, angles, and area ratios seen in vivo. Importantly, the model predicts that interfaces rich in E‑cadherin become shorter (strong adhesion dominates) while those enriched in N‑cadherin remain longer (weaker adhesion, higher cortical tension).

The robustness of the model was tested on several genetic perturbations. Over‑expression of E‑cadherin leads to a global reduction in interface length and a more circular cell shape, exactly as the simulation predicts when α_E is increased. Conversely, loss of N‑cadherin shortens the corresponding edges and yields a tighter packing, reproduced by decreasing α_N. The model also accommodates ommatidia with three or five cone cells: by simply changing the number of cells in the simulation while keeping the same α and β values, the resulting packing matches the experimentally observed triangular or pentagonal arrangements. Sensitivity analyses reveal that the ratio α_E/α_N determines the degree of asymmetry, whereas β controls overall cell compactness; extreme values of either parameter drive the system back toward a pure bubble‑like configuration or cause excessive collapse, respectively.

From a biological perspective, the work reframes cadherin function: rather than acting solely as a “glue” that reduces interfacial length, cadherins create additional adhesive surface that must be counterbalanced by cortical contractility. This competition defines the final geometry. The model therefore provides a quantitative bridge between molecular expression patterns and tissue‑scale mechanics, offering a framework that could be extended to other epithelia where multiple adhesion molecules coexist.

Limitations are acknowledged. The current formulation treats the eye as a two‑dimensional sheet, ignoring vertical deformations and the contribution of the underlying basement membrane. Moreover, the cortex is modeled as a simple isotropic contractile term, whereas real actomyosin networks exhibit spatial heterogeneity and active remodeling. Future work could integrate three‑dimensional finite‑element models, time‑resolved imaging of cadherin dynamics, and perturbations of actomyosin regulators to test the temporal predictions of the theory.

In summary, the authors demonstrate that a model combining adhesion‑driven surface increase with cortical contractility accurately reproduces both wild‑type and mutant Drosophila eye packing patterns, surpassing the explanatory power of the classic surface‑minimization (bubble) hypothesis. This study underscores the necessity of considering multiple, competing mechanical forces when interpreting how cells self‑organize into complex, functional tissues.