Computational analyses decipher the primordial folding coding the 3D structure of the beetle horn.

The beetle horn primordium is a complex and compactly folded epithelial sheet located beneath the larval cuticle. Only by unfolding the primordium can the complete 3D shape of the horn appear, suggesting that the morphology of beetle horns is encoded in the primordial folding pattern. To decipher the folding pattern, we developed a method to manipulate the primordial local folding on a computer and clarified the contribution of the folding of each primordium region to transformation. We found that the three major morphological changes (branching of distal tips, proximodistal elongation, and angular change) were caused by the folding of different regions, and that the folding mechanism also differs according to the region. The computational methods we used are applicable to the morphological study of other exoskeletal animals.