Statics and dynamics of the wormlike bundle model

Bundles of filamentous polymers are primary structural components
of a broad range of cytoskeletal structures, and their mechanical
properties play key roles in cellular functions ranging from
locomotion to mechanotransduction and fertilization. We give a
detailed derivation of a wormlike bundle model as a generic
description for the statics and dynamics of polymer bundles
consisting of semiflexible polymers interconnected by crosslinking
agents. The elastic degrees of freedom include bending as well as
twist deformations of the filaments and shear deformation of the
crosslinks. We show that a competition between the elastic
properties of the filaments and those of the crosslinks leads to
renormalized effective bend and twist rigidities that become
mode-number dependent. The strength and character of this
dependence is found to vary with bundle architecture, such as the
arrangement of filaments in the cross section and pretwist. We
discuss two paradigmatic cases of bundle architecture, a uniform
arrangement of filaments as found in F-actin bundles and a
shell-like architecture as characteristic for microtubules. Each
architecture is found to have its own universal ratio of maximal to
minimal bending rigidity, independent of the specific type of
crosslink-induced filament coupling; our predictions are in
reasonable agreement with available experimental data for
microtubules. Moreover, we analyze the predictions of the wormlike
bundle model for experimental observables such as the
tangent-tangent correlation function and dynamic response and
correlation functions. Finally, we analyze the effect of pretwist
(helicity) on the mechanical properties of bundles. We predict that
microtubules with different number of protofilaments should have
distinct variations in their effective bending rigidity.