  We present a novel platform for the large-scale simulation of fibrous
structures immersed in a Stokesian fluid and evolving under confinement or in
free-space. One of the main motivations for this work is to study the dynamics
of fiber assemblies within biological cells. For this, we also incorporate the
key biophysical elements that determine the dynamics of these assemblies, which
include the polymerization and depolymerization kinetics of fibers, their
interactions with molecular motors and other objects, their flexibility, and
hydrodynamic coupling.
  This work, to our knowledge, is the first technique to include many-body
hydrodynamic interactions (HIs), and the resulting fluid flows, in cellular
fiber assemblies. We use the non-local slender body theory to compute the
fluid-structure interactions of the fibers and a second-kind boundary integral
formulation for other rigid bodies and the confining boundary. A
kernel-independent implementation of the fast multiple method is utilized for
efficient evaluation of HIs. The deformation of the fibers is described by the
nonlinear Euler--Bernoulli beam theory and their polymerization is modeled by
the reparametrization of the dynamic equations in the appropriate
non-Lagrangian frame. We use a pseudo-spectral representation of fiber
positions and implicit HIs in the time-stepping to resolve large fiber
deformations, and to allow time-steps not constrained by temporal stiffness or
fiber-fiber interactions. The entire computational scheme is parallelized,
which enables simulating assemblies of thousands of fibers. We use our method
to investigate two important questions in the mechanics of cell division: (i)
the effect of confinement on the hydrodynamic mobility of microtubule asters;
and (ii) the dynamics of the positioning of mitotic spindle in complex cell
geometries.
