Applied Math Seminar

---

A coarse-grained model of microtubule hydrodynamics (and streaming flows in the fruit fly oocyte)

Speaker: David Stein, Flatiron Institute, (host: Shelley)

Location: TBA

Date: Friday, September 11, 2020, 2:30 p.m.

Synopsis:

An important class of fluid-structure problems involve the dynamics of ordered arrays of immersed, flexible fibers. While specialized numerical methods have been developed to study fluid-fiber systems, they become infeasible when there are many, rather than a few, fibers present, nor do these methods lend themselves to analytical calculation. Here, we introduce a coarse-grained continuum model, based on local-slender body theory, for elastic fibers immersed in a viscous Newtonian fluid. After exploring some basic properties of such ordered arrays, we use the model to study streaming flows in the fruit fly oocyte. In particular, we show that sufficiently dense microtubule arrays, forced only by molecular motors transporting cargo, undergo a "swirling transition" that is fundamentally different than the buckling transition which leads to the flapping motion of isolated filaments. The model produces streaming velocities consistent with in vivo measurements, and allows us to place bounds on the number density of kinesin-1 motors transporting cargo within the microtubule array.