A coarse-grained model of
microtubule hydrodynamics (and streaming flows in the fruit fly oocyte)
David Stein, Flatiron Institute
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.