Self-organized mechanochemical instabilities drive the emergence of digit tissue morphogenesis

The emergence of complex anatomical structures -such as the hands- from unstructured tissues remains a fundamental question in developmental biology. Turing-type reaction-diffusion models have provided a molecular explanation for the periodic pre-patterning of digits; however, the physical principles driving 3D morphogenesis remain incompletely understood. To identify the biophysical design principles leading to digit formation, we develop a limb-mesenchymal organoid system that spontaneously forms elongated, digit-like protrusions. Iterations between experiments and agent-based models at the cellular level identify sufficient microscopic mechanisms leading to morphogenesis of digit-like structures: symmetry-breaking and the elongation of digits result from a combination of differential cell adhesion and morphogen-induced chemotaxis and convergent-extension. Lastly, to describe tissue-scale deformations, we perform a coarse-graining analysis of the agent-based model and derive a continuum model that reveals a structural analogy to Cahn-Hilliard-type equations. These equations are typically used to describe fluid phase separation and so-called ''fingering instabilities'' in fluid physics. Here, we show that they also accurately describe organoid morphogenesis. These findings suggest that ''finger'' formation is driven by a mechanical fingering instability acting in concert with chemical patterning, shedding a new light on vertebrate limb morphogenesis.