  Buckling plays a critical role in the transport and dynamics of elastic
microfilaments in Stokesian fluids. However, previous work has only considered
filaments with homogeneous structural properties. Filament backbone stiffness
can be non-uniform in many biological systems like microtubules, where the
association and disassociation of proteins can lead to spatial and temporal
changes into structure. The consequences of such non-uniformities in the
configurational stability and transport of these fibers are yet unknown. Here,
we use slender-body theory and Euler-Bernoulli elasticity coupled with various
non-uniform bending rigidity profiles to quantify this buckling instability
using linear stability analysis and Brownian simulations. In shear flows, we
observe more pronounced buckling in areas of reduced rigidity in our
simulations. These areas of marked deformations give rise to differences in the
particle extra stress, indicating a nontrivial rheological response due to the
presence of these filaments. The fundamental mode shapes arising from each
rigidity profile are consistent with the predictions from our linear stability
analysis. Collectively, these results suggest that non-uniform bending rigidity
can drastically alter fluid-structure interactions in physiologically relevant
settings, providing a foundation to elucidate the complex interplay between
hydrodynamics and the structural properties of biopolymers.
