Tissue rigidity phase transition shapes morphogen gradients

During development, local mechanochemical cues within the cell microenvironment are translated into signalling pathways that drive cell fate decisions. Yet, as cells differentiate collectively, how global tissue-level properties shape these instructive cues remains unclear. Here we show that a tissue-scale rigidity transition guides patterning by tuning the length scales and timescales of morphogen signalling. By combining rigidity percolation theory, reaction-diffusion modelling, quantitative imaging and optogenetics in zebrafish, we uncover dynamical global tissue rigidity patterns that actively shape the Nodal morphogen gradient by locally changing its concentration and accelerating its signalling activity. In this self-generated mechanism, Nodal, besides instructing meso-endoderm fate specification, increases cell-cell adhesion strength via regulating planar cell polarity genes. Once the adhesion strength reaches a critical point, it triggers a rigidity transition which, in turn, induces the collapse of tissue porosity. The abrupt tissue reorganization negatively feeds back on Nodal signalling, impacting both its length scales, by restricting Nodal diffusivity, and its timescales, by speeding up the expression of its antagonist Lefty, thereby ensuring timely signal termination and robust patterning. Overall, we uncover a multiscale regulatory mechanism by which positional information and tissue material properties dynamically tune one another.