A mechano-chemical coupling drives fountain streaming and nuclear positioning in Drosophila embryos*

During early development of the syncytial embryo of Drosophila

melanogaster, the first nuclei go through successive division cycles

together with important cytoplasmic movement, driving the nuclei cloud

to expand along the anterior-posterior axis.

Previous experiments linking nuclei-produced PP1 to myosin-II

recruitment and flow activity, coupled with optogenetic manipulations,

have concluded that actomyosin cortical contractions are responsible for

this expansion. Still, the dynamics of the underlying long-range mechanochemical

coupling between nuclei and the cortex remains unexplored.

In this work, we lay the mathematical foundations of the hydrodynamic

flows, chemical couplings, and their interplay in the first seven cycles

of the development of Drosophila. We show that a two-fluid model,

considering a water-like incompressible phase (sol) and an active

elasto-viscous actin network (gel), captures the experimentally

observed sol flows and the uniform nuclei spreading by cell cycle seven

independently of natural variations in the initial nuclei position.

Numerical simulations predict a micron-sized cytosol boundary layer

close to the embryo cortex, and important differences in flow shape and

magnitude between sol and gel, paving the way to further experimental

methods and research.