Buckling without Bending

A New Paradigm in Morphogenesis

T. A. Engstrom, Teng Zhang, A. K. Lawton, A. L. Joyner, Jennifer M Schwarz

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 fluidlike 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 bioinspired applications, and address how our model is and is not unique to the developing nervous system.

Original languageEnglish (US)
Article number041053
JournalPhysical Review X
Volume8
Issue number4
DOIs
StatePublished - Dec 21 2018

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cerebellum
buckling
organs
fovea
elastic systems
nervous system
intestines
oscillations
radii
fibers
teeth
brain
invariance
tendencies
film thickness
gradients
microstructure

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Buckling without Bending : A New Paradigm in Morphogenesis. / Engstrom, T. A.; Zhang, Teng; Lawton, A. K.; Joyner, A. L.; Schwarz, Jennifer M.

In: Physical Review X, Vol. 8, No. 4, 041053, 21.12.2018.

Research output: Contribution to journalArticle

Engstrom, T. A. ; Zhang, Teng ; Lawton, A. K. ; Joyner, A. L. ; Schwarz, Jennifer M. / Buckling without Bending : A New Paradigm in Morphogenesis. In: Physical Review X. 2018 ; Vol. 8, No. 4.
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