An animal shape as an equilibrium*

A century ago, D’Arcy Thompson likened a jellyfish’s shape to the equilibrium form of a gelatinous drop. A recent finding that injured jellyfish reorganize and recover radial symmetry presented a tractable morphogenetic system in which to explore animal shape regulation after development. Performing grafting in Aurelia aurita, we explored how this system responds to different initial conditions. We found that slight changes in geometric initial condition led Aurelia to assume shapes such as circle, oval, trapezoid, square, and triangle, showing that radial symmetry is but one of many shapes this system can support. Further experiments and mathematical modeling suggested these shapes can be captured as equilibria of local force balancing, driven by muscle contractions and viscoelastic tissues. As the model predicts, increasing the rate of muscle contraction biases the solution toward radial symmetry. As expected for jellyfish shape as an equilibrium, Aurelia sequentially reorganized to rebalance new asymmetries. Maintaining animal shape as an equilibrium may facilitate evolvability. This finding may inspire self-organizing machinery that adapts to changing force landscapes.