A hydro-osmotic coarsening theory of biological cavity formation.

Fluid-filled biological cavities are ubiquitous, but their collective dynamics has remained largely unexplored from a physical perspective. Based on experimental observations in early embryos, we propose a model where a cavity forms through the coarsening of myriad of pressurized micrometric lumens, that interact by ion and fluid exchanges through the intercellular space. Performing extensive numerical simulations, we find that hydraulic fluxes lead to a self-similar coarsening of lumens in time, characterized by a robust dynamic scaling exponent. The collective dynamics is primarily controlled by hydraulic fluxes, which stem from lumen pressures differences and are dampened by water permeation through the membrane. Passive osmotic heterogeneities play, on the contrary, a minor role on cavity formation but active ion pumping can largely modify the coarsening dynamics: it prevents the lumen network from a collective collapse and gives rise to a novel coalescence-dominated regime exhibiting a distinct scaling law. Interestingly, we prove numerically that spatially biasing ion pumping may be sufficient to position the cavity, suggesting a novel mode of symmetry breaking to control tissue patterning. Providing generic testable predictions, our model forms a comprehensive theoretical basis for hydro-osmotic interaction between biological cavities, that shall find wide applications in embryo and tissue morphogenesis.