Numerical studies of microtubule-based motion in the single-celled C. elegans embryo

`Tamar Shinar, CIMS`

**Abstract:**

We develop a simple model of microtubule-based pronuclear motion
in a single-celled C. elegans embryo. The model consists of a model for microtubule
dynamic instability, a Newtonian, viscous fluid contained within an enclosing
geometry for the cytoplasm, a rigid body for the pronucleus,
and a motor protein load-velocity relationship.
Motor proteins distributed throughout the cytoplasm interact with
microtubule filaments by sliding along them with a velocity that depends on
their load. They in turn pull on the
filaments, resulting in translocation of the microtubule-bound pronucleus. I'll discuss
motivation and results for several numerical studies of this model.

I will also describe the numerical method for the coupled
simulation of the Stokes fluid and rigid body.
The method uses a background grid.
The physical domain is embedded in a periodic domain and no-slip
boundaries are treated as constraints.
The fluid operator resembles a boundary integral operator, but is not
formed explicitly, and its application has smaller asymptotic complexity than the
fully dense boundary integral operator.