Self-Similar Dynamics of Nuclear Packing in the Early Drosophila Embryo

Embryonic development starts with cleavages, a rapid sequence of reductive divisions that result in an exponential increase of cell number without changing the overall size of the embryo. In Drosophila, the final four rounds of cleavages occur at the surface of the embryo and give rise to ∼6000 nuclei under a common plasma membrane. We use live imaging to study the dynamics of this process and to characterize the emergent nuclear packing in this system. We show that the characteristic length scale of the internuclear interaction scales with the density, which allows the densifying embryo to sustain the level of structural order at progressively smaller length scales. This is different from nonliving materials, which typically undergo disorder-order transition upon compression. To explain this dynamics, we use a particle-based model that accounts for density-dependent nuclear interactions and synchronous divisions. We reproduce the pair statistics of the disordered packings observed in embryos and recover the scaling relation between the characteristic length scale and the density both in real and reciprocal space. This result reveals how the embryo can robustly preserve the nuclear-packing structure while being densified. In addition to providing quantitative description of self-similar dynamics of nuclear packings, this model generates dynamic meshes for the computational analysis of pattern formation and tissue morphogenesis.