Statics and Dynamics of the Wormlike Bundle Model

Abstract

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.

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• Cooperative crosslink (un)binding in slowly driven bundles of semiflexible filaments
• Crosslinked biopolymer bundles: crosslink reversibility leads to cooperative binding/unbinding phenomena
• Elasticity of cross-linked semiflexible biopolymers under tension
• Single-molecule stretching experiments of flexible (wormlike) chain molecules in different ensembles: Theory and a potential application of finite chain length effects to nick-counting in DNA
• Effect of grafting on the binding transition of two flexible polymers
• From particle condensation to polymer aggregation
• The asymptotic coarse-graining formulation of slender-rods, bio-filaments and flagella
• Back-Focal-Plane Imaging and Linear Density Measurements Of Sub-Diffraction Sized Biological Filaments and Particles
• Cross-linked pair of polymer chains under strong tension
• The counterbend dynamics of cross-linked filament bundles and flagella