Schematics showing possible variations of SC features and illustration of the Cellular Potts Model for simulation.

A Confocal images of ♂ wt (male wildtype) SC (labelled green) at 23 and 36 hours after pupariation. Each scale bar: 20 μm. B Schematic showing the rotation of SC. C Schematics showing three hypotheses for SC rotation: the push model (left) where SC rotates due to the force generated by the expanded distal cells, the pull model (centre) where SC rotates due to the pulling force generated by the contraction of proximal cells, and the push and pull model (right) where SC rotates due to both the pushing and pulling forces from the cells distally and proximally. D Schematics showing possible variations in SC orientations during evolution (top). Images of adult legs of Drosophila species that exemplify these variations (bottom). Each scale bar: 20 μm. E Schematics showing some possible variations in SC shapes during evolution (top). Images of adult legs of Drosophila species that exemplify these variations (bottom). Each scale bar: 20 μm. F Schematics showing possible variations in SC lengths during evolution (top). Images of adult legs of Drosophila species that exemplify these variations (bottom). Each scale bar: 20 μm. G Left: an example configuration of pixels in the Cellular Potts Model. Each square enclosed by dotted lines is a pixel (8 × 8 pixels in this configuration). The number inside the pixel represents the cell index label σ. Each pixel at a single time can only be labelled by one cell index. In this example there are 15 “cells” occupying 64 pixels at the current moment, and the solid lines represent “cell” boundaries. The colours of the cell index labels represent cell types c. Right: illustration of an attempted pixel label flip during a Monte Carlo step (mcs). The circled pixel on the left panel is the randomly chosen “target pixel”, and the pixel with a hexagon is the (also randomly chosen) neighbouring pixel (invading pixel). Whether there is a change to the cell index label of the target pixel is dependent on the relative effective energies of the configuration with and without the flipping. During a single mcs, there can be many such attempted pixel label flips (as specified by the parameters of the simulation–see Table 1). H Illustration of how variables θ and R are calculated for axial preference of epithelial cells. In this example, “cell” 11 is the “invading” cell (since the “invading” pixel belongs to that cell), and the “target” pixel is in cell 9. θ(σ = 11) is the angle subtended between the two vectors: the x axis and the vector that points from the centre of mass (CoM) of the “cell” 11 to the target pixel. R(σ = 11) is the norm of . In this example only θ(σ = 11) and R(σ = 11) are shown. Similarly, θ(σ = 9) (not labelled in this figure) is the angle subtended between the x axis and the vector that points from the CoM of cell 9 to the target pixel, while R(σ = 9) (again not labelled in this figure) is the norm of . I Left: an example initial cell configuration for a 9-tooth SC simulation. As in G and H, we use different colours to differentiate cell types (blue-EP1; magenta-EP2; yellow-EP3; green-SCT; red-BA), but the boundaries (black horizontal and vertical lines) depicted here are cell boundaries, not pixel boundaries. Right: blow-up of a selected rectangular area from the upper panel to illustrate cell types and sizes. In this magnification, there are four types of cells shown: EP1 (blue), EP3 (yellow), SCT (green) and BA (red). Cells of the same type may have different initial areas, as demonstrated by the blue EP1 cells. As an indication of the relative initial areas occupied by different cells, the (square) SC tooth marked with an “X” has an area of 6 × 6 = 36 pixels. “Proximal” refers to the region above the SC and “distal” refers to the region below the SC. Therefore, EP1 and EP2 cells are sometimes called “distal cells” but EP3 cells are sometimes called “proximal cells”.