Figure 1.

Morphogenesis of epithelial tissues in the absence of boundary constraints. (A) Model of an epithelial cell sheet. Each cell is represented by a polygon with four vertices denoted by solid circles. The shape of the cells is defined by the lengths of apical a_i (red), basal b_i (blue), and lateral ℓ_k (green) surfaces. A_i is the cross-sectional cell area. (B and C) Tissue shape changes under global modulation of the apical (B) or basal-lateral (C) mechanics. The epithelial sheet at the center (red box) is a flat sheet of columnar cells (N = 6) with an aspect ratio g = a/ℓ = 0.25 and an area A ≈ 0.89. The green and blue boxes highlight the morphological transitions resulting from changes of a given mechanical parameter. (D–G) Quantification of two morphological features of epithelial sheets. The curvature of the midplane (D and F) (see Appendix B for details) and the sheet thickness (E and G) are shown. The values a_oh, K_ah, λ_bh, and λ_ℓh are the mechanical parameters of the flat sheet, whereas Δq = q − q_h with q = a_o, K_a, λ_b, and λ_ℓ. To see this figure in color, go online.