Speaker
Description
Organism development occurs through sequences of astonishingly precise spatiotemporal changes, along which embryonic tissues switch between fluid- and solid-like states, arising from non-linear interactions among cellular constituents. In this context, tissue fluidization observed \textit{in vivo} in zebrafish embryos was interpreted, within the framework of rigidity percolation, as a rigid-to-floppy transition occurring at a critical point in cell connectivity. The microscopic parameters triggering these changes in cell connectivity, and whether they are interdependent, remain unclear. A density-driven rigidity transition is observed in \textit{wildtype} embryos at a critical cell fraction, $\phi_c$, marked by the emergence of a Giant Rigid Cluster (GRC), in which cell movements are hindered. Using genetic manipulations, we uncoupled the tissue material response from the jamming behaviour, generating living tissues displaying solid-like or fluid-like properties, although being unjammed or jammed, respectively. We explain this apparently paradoxical behaviour by analytically deriving a critical point in the relative surface tension, $\alpha_c$, beyond which a floppy motif of soft, adhesive spheres spontaneously rigidifies. Simulations of arbitrary arrays of cells, whose energy is described by a soap-bubble-like Hamiltonian, show a sharp transition in the GRC size at the predicted $\alpha_c$; a transition also observed in real embryonic tissues with cell fraction below the critical jamming fraction $\phi<\phi_c$. Embryonic tissues are thus characterized by a phase diagram organized around a double critical point ($\phi_c,\alpha_c$): when uncoupled from changes in cell fraction $\phi$, the relative surface tension $\alpha$ is the main control parameter of the tissue material properties. Furthermore, at the critical point $\alpha_c$ at which adhesion-driven rigidification takes place, a sudden formation of tricellular contacts is observed, dictating an abrupt tissue reorganization and defining a transition from a non-confluent to a fully confluent regime. Our theoretical and experimental results show how basic physical parameters have far-reaching roles in tissue architecture, properties, and functions.
