Rigidity percolation uncovers a structural basis for embryonic tissue phase transitions

Summary Embryo morphogenesis is impacted by dynamic changes in tissue material properties, which have been proposed to occur via processes akin to phase transitions (PTs). Here, we show that rigidity percolation provides a simple and robust theoretical framework to predict material/structural PTs of embryonic tissues from local cell connectivity. By using percolation theory, combined with directly monitoring dynamic changes in tissue rheology and cell contact mechanics, we demonstrate that the zebrafish blastoderm undergoes a genuine rigidity PT, brought about by a small reduction in adhesion-dependent cell connectivity below a critical value. We quantitatively predict and experimentally verify hallmarks of PTs, including power-law exponents and associated discontinuities of macroscopic observables. Finally, we show that this uniform PT depends on blastoderm cells undergoing meta-synchronous divisions causing random and, consequently, uniform changes in cell connectivity. Collectively, our theoretical and experimental findings reveal the structural basis of material PTs in an organismal context.
Graphical abstract
Highlights • Zebrafish morphogenesis starts with a tissue rigidity phase transition • Percolation theory predicts this transition based on the cell connectivity network • Cell-cell adhesion defines the cell connectivity network and thus tissue rigidity • Cell-cycle synchrony ensures a uniform transition by randomly changing connectivity
A general theoretical approach, rooted in cell connectivity, enables prediction of phase transitions at the tissue scale.