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

Abstract

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 densitydependent 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.

Attractive internuclear force drives the collective behavior of nuclear arrays inDrosophilaembryos

“…For example, the model in ref. (Dutta et al, 2019) cannot generate any collective motion at all. The model in ref.…”

“…Further experiments are still needed to test this speculation directly. data, the nuclear array has no long-range positional order, nor is amorphous (Dutta et al, 2019). And based on the KTHNY theory (Zippelius et al, 1980, Strandburg, 1988, Halperin and Nelson, 1978, during S phase the nuclear array is the liquid state because of the topological defects (5 nuclear neighbors or 6 nuclear neighbors) (Kanesaki et al, 2011) and exponential decay of the hexatic correlation function (Kaiser et al, 2018).…”

“…And previous studies also show distance-dependent force fields are needed to stabilize the nuclear array on the ellipsoid surface (Dutta et al, 2019). And the distance-dependent force field usually has a "core region" and a "border region" (Dutta et al, 2019). Based on the F a force assumption, the core region consists of the actin caps.…”

“…After each nuclear cycle, the density of the nuclear array doubles, and the internuclear distance decreases. The spatial and orientation order increase from early to later nuclear cycles (Kaiser et al, 2018), but the radial distribution functions overlap if they are rescaled with the nuclear density (Dutta et al, 2019). At the end of each nuclear cycle, a persuade-synchronized mitotic wave usually starts from the two embryo poles, moves towards the equator of the embryo along the anterior-posterior (AP) axis.…”

“…Several particle-based models have been proposed with different formulas of the pair-wise force between nuclei (Kaiser et al, 2018, Dutta et al, 2019, Lv et al, 2020.…”