Fig. 3: Thickness-curvature coupling arises due to apico-basal polarity.

a, b Thickness-curvature portraits of the active T1 (\({k}_{{\rm{T}}1}^{(0)}=200\)) budded shape with α = 1.1, β = 0.5 (a) and of a stomatocyte shape with α = 0.5, β = 1.1 (b); each cell is represented by a point. In the cutaway view of the model epithelial shells, tissue thickness is represented using color code, which is also used for the points in the two diagrams. c Modulation of tissue thickness δ in shapes in the (α, β)-plane for \({k}_{{\rm{T}}1}^{(0)}=200\). The gray region represents the non-physical regime, whereas the hatched region denotes the spherical shapes at α + β > 2.6. d The 56,400 cell-by-cell h(c) datapoints from the 188 model shapes from panel c with α + β < 1.9. e Datapoints from panel d collapsed by rescaling described in the text; also plotted is the line of identity.