Mechanical Model of Nuclei Ordering in Drosophila Embryos Reveals Dilution of Stochastic Forces

During the initial development of syncytial embryos, nuclei go through cycles of nuclear division and spatial rearrangement. The arising spatial pattern of nuclei is important for subsequent cellularization and morphing of the embryo. Although nuclei are contained within a common cytoplasm, cytoskeletal proteins are nonuniformly packaged into regions around every nucleus. In fact, cytoskeletal elements like microtubules and their associated motor proteins exert stochastic forces between nuclei, actively driving their rearrangement. Yet, it is unknown how the stochastic forces are balanced to maintain nuclear order in light of increased nuclear density upon every round of divisions. Here, we investigate the nuclear arrangements in Drosophila melanogaster over the course of several nuclear divisions starting from interphase 11. We develop a theoretical model in which we distinguish long-ranged passive forces due to the nuclei as inclusions in the elastic matrix, namely the cytoplasm, and active, stochastic forces arising from the cytoskeletal dynamics mediated by motor proteins. We perform computer simulations and quantify the observed degree of orientational and spatial order of nuclei. Solely doubling the nuclear density upon nuclear division, the model predicts a decrease in nuclear order. Comparing results to experimental recordings of tracked nuclei, we make contradictory observations, finding an increase in nuclear order upon nuclear divisions. Our analysis of model parameters resulting from this comparison suggests that overall motor protein density as well as relative active-force amplitude has to decrease by a factor of about two upon nuclear division to match experimental observations. We therefore expect a dilution of cytoskeletal motors during the rapid nuclear division to account for the increase in nuclear order during syncytial embryo development. Experimental measurements of kinesin-5 cluster lifetimes support this theoretical finding.