Numerical studies of microtubule-based motion in the single-celled C. elegans embryo
Tamar Shinar, CIMS
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.