Morphoelastic modelling of pattern development in the petal epidermal cell cuticle.

We use the model system as a vehicle to study the origin and propagation of surface nano-ridges in plant petal epidermal cells by tracking the development of the cell shape and the cuticle. In this system, the cuticle develops two distinct sub-layers, (i) an uppermost layer which increases in thickness and in-plane extension and (ii) a substrate, composed of cuticular and cell wall material. We quantify the pattern formation and geometrical changes and then postulate a mechanical model assuming that the cuticle behaves as a growing bi-layer. The model is a quasi-static morphoelastic system and it is numerically investigated in two- and three-dimensional settings, using different laws of film and substrate expansion and boundary conditions. We recreate several features of the observed developmental trajectories in petals. We establish the respective roles of the layers' stiffness mismatch, the underlying cell-wall curvature, the cell in-plane expansion and the thickness growth rates of the layers in determining the observed pattern features, such as the variance observed in the amplitude and wavelength of the cuticular striations. Our observations provide evidence which justifies the growing bi-layer description, and provide valuable insights into why some systems develop surface patterns and others do not.