A coarse-grained model for cytoplasmic streaming

Cytoplasmic streaming is a striking example of fluid-structure interactions within living cells. Egg cells are among the largest, and transporting by diffusion of the proteins necessary for their development is extremely slow. In the later stages of the developing fruit fly egg, a coherent circulatory flow emerges that spans the entire ~200 μm scale cell. This streaming flow is driven by the motion of nanometric motors transporting subcellular cargo along stiff biopolymers (microtubules) anchored at the cell wall. Streaming is crucial for the organism's development, but exactly what functions are fulfilled remains unclear. Here we theoretically investigate the transition to streaming and the consequent transport and mixing. For this, we use a coarse-grained continuum theory that captures the collective response of microtubules and motors that drive the internal flows. This model has the form of a boundary force field fully coupled to an internal Stokesian flow. In particular, we study how the flow line topology is influenced by microtubule density and the geometry of the egg cell, as well as first-passage times from sources to sinks.