Buckling without bending: a new paradigm in morphogenesis

Abstract

A curious feature of organ and organoid morphogenesis is that in certain cases, spatial oscillations in the thickness of the growing "film" are out-of-phase with the deformation of the slower-growing "substrate," while in other cases, the oscillations are in-phase. The former cannot be explained by elastic bilayer instability, and contradict the notion that there is a universal mechanism by which brains, intestines, teeth, and other organs develop surface wrinkles and folds. Inspired by the microstructure of the embryonic cerebellum, we develop a new model of 2d morphogenesis in which system-spanning elastic fibers endow the organ with a preferred radius, while a separate fiber network resides in the otherwise fluid-like film at the outer edge of the organ and resists thickness gradients thereof. The tendency of the film to uniformly thicken or thin is described via a "growth potential". Several features of cerebellum, +blebbistatin organoid, and retinal fovea morphogenesis, including out-of-phase behavior and a film thickness amplitude that is comparable to the radius amplitude, are readily explained by our simple analytical model, as may be an observed scale-invariance in the number of folds in the cerebellum. We also study a nonlinear variant of the model, propose further biological and bio-inspired applications, and address how our model is and is not unique to the developing nervous system.

arXiv commentversion accepted by Physical Review X

References in corpus (5)

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Cited by in corpus (10)

• Surface tension controls the onset of gyrification in brain organoids
• The mechanics of human brain organoids
• Nonlinear and Nonlocal Elasticity in Coarse-Grained Differential-Tension Models of Epithelia
• Wrinkling instability in unsupported epithelial sheets
• Buckling without bending morphogenesis: Nonlinearities, spatial confinement, and branching hierarchies
• Retina organoids: Window into the biophysics of neuronal systems
• Large-scale cortex-core structure formation in brain organoids
• (Un)buckling mechanics of epithelial monolayers under compression
• Localised bifurcation in soft cylindrical tubes under axial stretching and surface tension
• Buckling by disordered growth