Figure 5
From: Computational analyses decipher the primordial folding coding the 3D structure of the beetle horn
The furrow in the cap actively shapes the four-branched structure. (a) Superimposed drawing of the cap before and after expansion with the angle adjusted (viewed from the ventral side). The unfolded cap had a four-branched shape (white mesh), while the folded cap had a dome-like shape (red mesh). (b,c) Based on the unfolded shape, the cap was subdivided into four subregions: medial tips, lateral tips, upper surface, and bottom surface (colored in white, red, pink, and green, respectively). The area in the folded primordia corresponding to each subregion was identified in the correspondence analysis. (d–g) Furrow visualization of the cap. The direction of the yellow double-headed arrows is the estimated extending direction (perpendicular to the furrows). (d) In medial tips, the furrow pattern was a concentric semicircular pattern. (e) In lateral tips, the furrows had no distinct directionality. (f) The upper surface had bow-shaped furrows facing each other, like hyperbolas. (g) On the bottom surface, many parallel linear furrows run in the dorsoventral direction. (d′–g′) Furrow removal analysis of the cap. The difference between the cross-sections of the unfolded original mesh (white lines) and the unfolded smoothed mesh (red lines) showed the function of the furrows. (d′,e′) When the furrow pattern was removed, the medial tips became much smaller than the original ones (d′, yellow arrows), while the shape of the lateral tips changed little (e′). (f′,g′) Furrow removal on the upper surface made the angle of the central groove smaller (f′, yellow arrows), while that of the bottom surface made the angle of the central groove bigger (g′, yellow arrows). (h–k) Difference between perfect concentric circles and concentric semicircles. When expanded, the perfect circles formed a cone perpendicular to the plane (i), while the concentric semicircles had an oblique cone overhang (k). (l) Schematic diagram of the furrow patterns and shape change. The contribution of the furrows allows the primordial dome-like shape to transform into the pupal four-branched shape.
