Fig 1.
Schematic view of one of the exemplarily investigated feedback-loops between tissue mechanics and morphogen production.
Local morphogen levels lead to apical constriction in biological cells, which leads (due to the elastic response of the tissue maintaining continuity) to local stretch, which induces again local morphogen production.
Fig 2.
(A)-(B) Simulation snapshots showing spontaneous pattern formation based on a simple mechanochemical feedback loop including basal constriction. In (B), the 3D tissue body has been sliced just for the purpose of a better visualisation. An experimental example showing co-localisation of tissue curvature and morphogen concentration during Hydra development can be e.g. found in Ref. [104].
Fig 3.
(A)-(B) Simulation snapshots showing spontaneous pattern formation based on a simple mechanochemical feedback loop including apical constriction. In (B), the 3D tissue body has been sliced just for the purpose of a better visualisation. (C) Microscopic pictures showing similar morphogen and curvature patterns in Nematostella during gastrulation (with permission from Ref. [76]).
Fig 4.
Simulation snapshots investigating the robustness of mechanochemical patterns with respect to (A) a thicker tissue layer (doubled thickness); (B) a thinner tissue layer (halved thickness); (C) a smaller system (384 biological cells); (D) lower tangential diffusion (quartered); (E) without any tangential diffusion; and (F) basal constriction only in the outer half of biological cells.
Fig 5.
(A) Schematic view of the multiplicative decomposition of the deformation gradient tensor. (B) Numerical versus biological cells in the reference configuration (left-hand side) and an example of the deformed simulated tissue body with chemical (morphogen) patterns (right-hand side). Purple color represents high, white color low local morphogen levels. The 3D tissue body has been sliced just for the purpose of a better visualisation.