Four-Fold Order and Shape Formation in Parhyale Embryo

Abstract

The generation of six-fold order structures has been well studied in both active and non-active matter systems. We are interested in the formation of four-fold lattice structure in the epithelial cells of a growing crustacean embryo. An example of an active matter system, the Parhyale hawaiensis embryo is an ensemble of living cells that converts chemical energy into work driving shape generation and pattern formation despite noise and being far from thermodynamic equilibrium. Unlike 2D hexagon-dominated topologies, rectangular lattices are rare due to its structural instability, and their emergence cannot be explained by cell packing or randomly-oriented divisions. We extract meaningful physical observables such as cell trajectories and tissue strain-rates from the growing embryo using light-sheet microscopy and computer vision. By analyzing mechanical properties, we can predict the development of the embryo, including order formation and tissue folding. In particular, we show how four-fold order can arise and be preserved via actively choreographed cell division patterns in such a way that no additional stresses accumulate in tissue during the onset of ordering.