Mechanochemical coupling enables propagating patterns without diffusion

Morphogenesis and morphological events during embryo development involve coordinated cell and tissue shape changes. They are driven by mechanical forces, which in turn are triggered by complex chemical signaling. The chemical signals form gradients that provide positional information in the tissue, and in principle are also dependent on mechanical state of cells. Using mathematical modeling, we demonstrate how chemical signaling coupled with long-range buckling deformations can induce dynamic spatial patterns in an elastic shell even without a diffusive or advective transport of the chemicals. This mechanism is a complementary proposal to the Turing patterns, but it does not require interactions between multiple chemical species with very different diffusivity. We demonstrate that depending on key parameters, for example the threshold in activation of cell's mechanical response or the shell thickness, the mechanochemical feedback gives rise to qualitatively different deformation patterns such as ridges and spots that are robust to changes in shell geometry. Our findings open new routes to designing an excitable medium with tunable pattern formation that has potential applications in tissue engineering and fabrication of functional surfaces.