  Thermal fluctuations of microtubules (MTs) and other cytoskeletal filaments
govern to a great extent the complex rheological properties of the cytoskeleton
in eukaryotic cells. In recent years, much effort has been put into capturing
the dynamics of these fluctuations by means of analytical and numerical models.
These attempts have been very successful for, but also remain limited to,
isotropic polymers. To correctly interpret experimental work on (strongly)
anisotropic semiflexible polymers, there is a need for a numerical modelling
tool that accurately captures the dynamics of polymers with anisotropic
material properties. In the current study, we present a finite element (FE)
framework for simulating the thermal dynamics of a single anisotropic
semiflexible polymer. First, we demonstrate the accuracy of our framework by
comparison of the simulated mean square displacement (MSD) of the end-to-end
distance with analytical predictions based on the worm-like chain model. Then,
we implement a transversely isotropic material model, characteristic for
biopolymers such as MTs, and study the persistence length for various ratios
between the longitudinal shear modulus and corresponding Young's modulus.
Finally, we put our findings in context by addressing a recent experimental
work on grafted transversely isotropic MTs. In that research, a simplified
static mechanical model was used to deduce a very high level of MT anisotropy
to explain the observation that the persistence length of grafted MTs increases
as contour length increases. We show, by means of our FE framework, that the
anisotropic properties cannot account for the reported length-dependent
persistence length.
